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Dissertations / Theses on the topic 'Three-manifolds'
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1
Mijatović, Aleksandar. "Triangulations of three-manifolds." Thesis, University of Cambridge, 2003. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.619611.
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Newman-Gomez, Sharon Angela. "State sum invariants of three manifolds." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1510.
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Cremaschi, Tommaso. "Hyperbolic 3-manifolds of infinite type:." Thesis, Boston College, 2019. http://hdl.handle.net/2345/bc-ir:108468.
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Thesis advisor: Ian BiringerIn this thesis we study the class of 3-manifolds that admit a compact exhaustion by hyperbolizable 3-manifolds with incompressible boundary and such that the genus of the boundary components of the elements in the exhaustion is uniformly bounded. For this class we give necessary and sufficient topological conditions that guarantee the existence of a complete hyperbolic metric
Thesis (PhD) — Boston College, 2019
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
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Wang, Bai-Ling. "Seiberg-Witten monopoles on three-manifolds /." Title page, abstract and contents only, 1997. http://web4.library.adelaide.edu.au/theses/09PH/09phw2455.pdf.
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Howards, Hugh Nelson. "Curves and surfaces in three-manifolds /." Diss., Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 1997. http://wwwlib.umi.com/cr/ucsd/fullcit?p9732691.
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Braam, Peter J. "Magnetic monopoles and hyperbolic three-manifolds." Thesis, University of Oxford, 1987. http://ora.ox.ac.uk/objects/uuid:daa73d43-6d58-404c-9926-ebf23f59cfc6.
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Let M = H3/Γ be a complete, non-compact, oriented geometrically finite hyperbolic 3-manifold without cusps. By constructing a conformal compactification of M x S1 we functorially associate to M an oriented, conformally flat, compact 4-manifold X (without boundary) with an S1-action. X determines M as a hyperbolic manifold. Using our functor and the differential geometry of conformally flat 4-manifolds we prove that any Γ as above with a limit set of Hausdorff dimension ≤ 1 is Schottky, Fuchsian or extended Fuchsian. Furthermore, the Hodge theory for H2 (X;R) carries over to H1(M, δM;R) and H2(M;R) which correspond to the spaces of harmonic L2-forms of degree 1 and 2 on M. Comparison of lattices through the Hodge star gives an invariant h(M) ε GL(H2(M;R)/GL(H2(M;Z)) of the hyperbolic structure. Secondly we pay attention to magnetic monopoles on M which correspond to S1invariant solutions of the anti-self-duality equations on X. The basic result is that we associate to M an infinite collection of moduli spaces of monopoles , labelled by boundary conditions. We prove that the moduli spaces are not empty (under reasonable conditions), compute their dimension , prove orientability , the existence of a compactification and smoothness for generic S1-invariant conformal structures on X. For these results one doesn't need a hyperbolic structure on M , the existence of a conformal compactification X suffices. A twistor description for monopoles on a hyperbolic M can be given through the twistor space of X , and monopoles turn out to correspond to invariant holomorphic bundles on twistor space. We analyse these bundles. Explicit formulas for monopoles can be found on handlebodies M , and for M = surface x R we describe the moduli spaces in some detail.
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Haynes, Elizabeth Lydia. "Smale Flows on Three Dimensional Manifolds." OpenSIUC, 2012. https://opensiuc.lib.siu.edu/dissertations/470.
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We discuss how to realize simple Smale Flows on 3-manifolds. We focus on three questions: (1) What are the topological conjugate classes of Lorenz Smale flows that can be realized on S3? (2) Which 3-manifolds can also admit a Lorenz Smale flow? (3) What are the topological conjugate classes of simple Smale flows whose saddle set can be modeled by &nu(0+,0+,0,0) can be realized on S3? This dissertation extends the work of M. Sullivan and B. Yu.
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Breinlinger, Keith J. (Keith Joseph) 1974. "Three-dimensional routed manifolds with externally inserted cables." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/29624.
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Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2003.Includes bibliographical references (p. 253-259).
The Automatic Test Equipment industry must maintain a tester accuracy of roughly one tenth the pulsewidth of the device under test (DUT). Funneling a vast number of electrical signals into a very tiny area to contact the DUT while still maintaining good signal fidelity is a problem not only in the ATE industry, but also for personal computers, network servers and supercomputers. As the speed of processors increase, ATE companies must find new ways to achieve the required accuracy. A solution to this problem is investigated whereby a large number of semi-rigid coaxial wires are routed in 3D space from a low-density array (the tester side) to a high-density array (the DUT side). The three dimensional paths are subject to bend constraints and cannot intersect with any other paths. A software program has been written and tested that is able to find solutions to this 3D routing problem for many test cases. For relatively simple test cases with less than 15 wires, solutions can typically be found in under a minute. Once the geometries of the paths are determined, a block is made with 3D tunnels transversing through it. This part is created using a 3D additive process (e.g. stereolithography), and the coaxial wires are pushed into each tunnel. The maximum force used to insert a wire into a tunnel is limited by the force at which buckling occurs. Uncontrolled buckling of the coaxial wire will compromise electrical signal fidelity or cause opens and must therefore be prevented. To this end, models have been developed to predict the force required to push wires into a predetermined path. Relatively good experimental agreement, within 20% in many cases, was achieved for paths with radii of curvature to wire diameter ratios between 200:1 and 10:1. A perfectly elastic beam model is developed as well as an elastic-plastic beam model.
(cont.) Additional models are developed which account for the friction and the effect of clearance between the tunnel and the beam. The model is used to guide the routing software such that no path is created that cannot have a wire inserted into it. The solution proposed provides an excellent alternative to a printed circuit board for high speed electrical signals. The general method of using additive manufacturing to create tunnels to guide signal opens up many possibilities for not just coaxial cables, but fluid piping, optical fibers and solid wires. The solution has many further advantages and applications that are reviewed briefly but have not been investigated.
by Keith J. Breinlinger.
Ph.D.
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Adhikari, Kamal Mani. "Realizations of simple Smale flows on three-manifolds." OpenSIUC, 2016. https://opensiuc.lib.siu.edu/dissertations/1250.
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In this dissertation, we discuss how to realize simple Smale flows on 3-manifolds. We use four-band and three-band templates to study the linking structure of two types of closed orbits known as attracting closed orbits and repelling closed orbits in the flow. This dissertation extends the work done by M. Sullivan on realizing Lorenz Smale flows on 3-manifolds, by Bin Yu on realizing Lorenz-like Smale flows on 3-manifolds and continues the work of Elizabeth Haynes and Michael Sullivan on realizing simple Smale flows with a four-band template on a 3-sphere. The four-band template we use in this dissertation is different from the template used by Haynes and Sullivan.
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Alcaraz, Karin. "The Alexander polynomial of closed 3-manifolds." Thesis, University of Oxford, 2011. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.564280.
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Clement, Juan Souto Kleineidam Gero. "Geometric structures on 3-manifolds and their deformations." Bonn : Mathematisches Institut der Universität, 2001. http://catalog.hathitrust.org/api/volumes/oclc/52313822.html.
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Marcotte, Cynthia Janet Verjovsky. "Essential surfaces after Dehn filling /." Full text (PDF) from UMI/Dissertation Abstracts International, 2000. http://wwwlib.umi.com/cr/utexas/fullcit?p9992864.
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Durusoy, Daniel Selahi. "Heegaard Floer homology of certain 3-manifolds and cobordism invariants." Diss., Connect to online resource - MSU authorized users, 2008.
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Casey, Meredith Perrie. "Branched covers of contact manifolds." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50313.
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We will discuss what is known about the construction of contact structures via branched covers, emphasizing the search for universal transverse knots. Recall that a topological knot is called universal if all 3-manifold can be obtained as a cover of the 3-sphere branched over that knot. Analogously one can ask if there is a transverse knot in the standard contact structure on S³ from which all contact 3-manifold can be obtained as a branched cover over this transverse knot. It is not known if such a transverse knot exists.
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Neil, John Ralph. "Tunnel One Generalized Satellite Knots." PDXScholar, 1995. https://pdxscholar.library.pdx.edu/open_access_etds/1273.
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In 1984, T. Kobayashi gave a classification of the genus two 3-manifolds with a nontrivial torus decomposition. The intent of this study is to extend this classification to the genus two, torally bounded 3-manifolds with a separating non-trivial torus decomposition. These 3-manifolds are also known as the tunnel-1 generalized satellite knot exteriors. The main result of the study is a full decomposition of the exterior of a tunnel-1 satellite knot in an arbitrary 3-manifold. Several corollaries are drawn from this classification. First, Schubert's 1953 results regarding the existence and uniqueness of a core component for satellite knots in the 3-sphere is extended to tunnel-1 satellite knots in arbitrary 3-manifolds. Second, Morimoto and Sakuma's 1991 classification of tunnel-1 satellite knots in the 3-sphere is extended to a classification of the tunnel-1 satellite knots in lens spaces. Finally, for these knot exteriors, a result of Eudave-Muñoz in 1994 regarding the relative position of tunnels and decomposing tori is recovered.
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Blumen, Sacha Carl. "Quantum Superalgebras at Roots of Unity and Topological Invariants of Three-manifolds." University of Sydney. School of Mathematics and Statistics, 2005. http://hdl.handle.net/2123/715.
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The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudomodular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular Hopf algebra. The quantum superalgebra Uq(osp(1|2n)) over C is considered with q a primitive Nth root of unity for all integers N > = 3. For such a q, a certain left ideal I of U_q(osp(1|2n)) is also a two-sided Hopf ideal, and the quotient algebra U^(N)_q(osp(1|2n)) = U_q(osp(1|2n))/I is a Z_2-graded ribbon Hopf algebra. For all n and all N > = 3, a finite collection of finite dimensional representations of U^(N)_q(osp(1|2n)) is defined. Each such representation of U^(N)_q(osp(1|2n)) is labelled by an integral dominant weight belonging to the truncated dominant Weyl chamber. Properties of these representations are considered: the quantum superdimension of each representation is calculated, each representation is shown to be self-dual, and more importantly, the decomposition of the tensor product of an arbitrary number of such representations is obtained for even N. It is proved that the quotient algebra U(N)^q_(osp(1|2n)), together with the set of finite dimensional representations discussed above, form a pseudo-modular Hopf algebra when N > = 6 is twice an odd number. Using this pseudo-modular Hopf algebra, we construct a topological invariant of 3-manifolds. This invariant is shown to be different to the topological invariants of 3-manifolds arising from quantum so(2n+1) at roots of unity.
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Masters, Joseph David. "Lengths and homology of hyperbolic 3-manifolds /." Digital version accessible at:, 1999. http://wwwlib.umi.com/cr/utexas/main.
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Jarabek, Raquel L. "Investigation of manifolds and optimized trajectories in the three-body problem." College Park, Md. : University of Maryland, 2004. http://hdl.handle.net/1903/2120.
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Thesis (M.S.) -- University of Maryland, College Park, 2004.Thesis research directed by: Dept. of Aerospace Engineering. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Thomas, Joseph. "Conformal Variations of Piecewise Constant Curvature Two and Three Dimensional Manifolds." Diss., The University of Arizona, 2015. http://hdl.handle.net/10150/560854.
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Piecewise constant curvature manifolds are discrete analogues of Riemannian manifolds in which edge lengths play the role of the metric tensor. These triangulated manifolds are specified by two types of data: 1. Each edge in the triangulation is assigned a real-valued length. 2. For each simplex in the triangulation, there exists an isometric embedding of that simplex into one of three background geometries (Euclidean, hyperbolic, or spherical). In particular, this isometry respects the edge length data. By making the edge lengths functions of scalars, called conformal parameters, that are assigned to the vertices of the triangulation we obtain a conformal structure - that is, a parameterization of a discrete conformal class. We discuss how our definition of conformal structure places several existing notions of a discrete conformal class in a common framework. We then describe discrete analogues of scalar curvature for 2-and 3-manifolds and study how these curvatures depend on the conformal parameters. This leads us to some local rigidity theorems - we identify circumstances in which the mapping from conformal parameters to scalar curvatures is a local diffeomorphism. In three dimensions, we focus on the case of hyperbolic background geometry. We study a discrete analogue of the Einstein-Hilbert (or total scalar curvature) functional and investigate when this functional is locally convex.
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Ross, Shane David Marsden Jerrold E. "Cylindrical manifolds and tube dynamics in the restricted three-body problem /." Diss., Pasadena, Calif. : California Institute of Technology, 2004. http://resolver.caltech.edu/CaltechETD:etd-05182004-154045.
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Difonzo, Fabio Vito. "The Filippov moments solution on the intersection of two and three manifolds." Diss., Georgia Institute of Technology, 2015. http://hdl.handle.net/1853/54388.
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In this thesis, we study the Filippov moments solution for differential equations with discontinuous right-hand side. In particular, our aim is to define a suitable Filippov sliding vector field on a co-dimension $2$ manifold $\Sigma$, intersection of two co-dimension $1$ manifolds with linearly independent normals, and then to study the dynamics provided by this selection. More specifically, we devote Chapter 1 to motivate our interest in this subject, presenting several problems from control theory, non-smooth dynamics, vehicle motion and neural networks. We then introduce the co-dimension $1$ case and basic notations, from which we set up, in the most general context, our specific problem. In Chapter 2 we propose and compare several approaches in selecting a Filippov sliding vector field for the particular case of $\Sigma$ nodally attractive: amongst these proposals, in Chapter 3 we focus on what we called \emph{moments solution}, that is the main and novel mathematical object presented and studied in this thesis. There, we extend the validity of the moments solution to $\Sigma$ attractive under general sliding conditions, proving interesting results about the smoothness of the Filippov sliding vector field on $\Sigma$, tangential exit at first-order exit points, uniqueness at potential exit points among all other admissible solutions. In Chapter 4 we propose a completely new and different perspective from which one can look at the problem: we study minimum variation solutions for Filippov sliding vector fields in $\R^{3}$, taking advantage of the relatively easy form of the Euler-Lagrange equation provided by the analysis, and of the orbital equivalence that we have in the eventuality $\Sigma$ does not have any equilibrium points on it; we further remove this assumption and extend our results. In Chapter 5 examples and numerical implementations are given, with which we corroborate our theoretical results and show that selecting a Filippov sliding vector field on $\Sigma$ without the required properties of smoothness and exit at first-order exit points ends up dynamics that make no sense, developing undesirable singularities. Finally, Chapter 6 presents an extension of the moments method to co-dimension $3$ and higher: this is the first result which provides a unique admissible solution for this problem.
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Garza, César. "Examples of hyperbolic knots with distance 3 toroidal surgeries in S³." To access this resource online via ProQuest Dissertations and Theses @ UTEP, 2009. http://0-proquest.umi.com.lib.utep.edu/login?COPT=REJTPTU0YmImSU5UPTAmVkVSPTI=&clientId=2515.
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Hayden, Kyle. "Knot theory of holomorphic curves in Stein surfaces." Thesis, Boston College, 2018. http://hdl.handle.net/2345/bc-ir:107925.
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Thesis advisor: John A. BaldwinWe study the relationship between knots in contact three-manifolds and complex curves in Stein surfaces. To do so, we extend the notion of quasipositivity from classical braids to links that are braided with respect to an open book decomposition of an arbitrary closed, oriented three-manifold. Our main results characterize the transverse links in Stein-fillable contact three-manifolds that bound smooth holomorphic curves in Stein fillings. This characterization is made possible by new techniques in the theory of characteristic and open book foliations on surfaces in three-manifolds. We also explore the Seifert genera of cross-sections of complex plane curves, minimal braid representatives of quasipositive links, and the relationship between Legendrian ribbons in contact three-manifolds and strongly quasipositive braids with respect to compatible open books
Thesis (PhD) — Boston College, 2018
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
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Mullins, Larry Andrew. "An upperbound on the ropelength of arborescent links." CSUSB ScholarWorks, 2007. https://scholarworks.lib.csusb.edu/etd-project/3133.
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PENAFIEL, CARLOS DIOSDADO ESPINOZA. "SURFACES OF CONSTANT MEAN CURVATURE IN HOMOGENEOUS THREE MANIFOLDS WITH EMPHASIS IN GPSL2(R, Τ )." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2010. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=16214@1.
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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIORFUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
Nesta teses, nós estudamos H-superfícies, isto é, superfícies tendo curvatura media constante, imersas em variedades homogêneas simplesmente conexas de dimensão 3. Nós focamos nossa atenção no estudo de existência de H multigráficos. Também estudamos a H-superfícies invariantes por um grupo a um parâmetro de isometrias que estão imersas no espaço PSL(2) (R, T).
In this thesis we study H-surfaces, that is, surfaces having constant mean curvature, immersed in homogeneous simply connected 3-manifold. We focus our attention in the study of existence of H multigraphs. We also study the H-surfaces invariant by one-parameter group of isometries which are immersed in the space]PSL2(R, T).
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Cengiz, Mustafa. "Heegaard Splittings and Complexity of Fibered Knots:." Thesis, Boston College, 2020. http://hdl.handle.net/2345/bc-ir:108729.
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Thesis advisor: Tao LiThis dissertation explores a relationship between fibered knots and Heegaard splittings in closed, connected, orientable three-manifolds. We show that a fibered knot, which has a sufficiently complicated monodromy, induces a minimal genus Heegaard splitting that is unique up to isotopy. Moreover, we show that fibered knots in the three-sphere has complexity at most 3
Thesis (PhD) — Boston College, 2020
Submitted to: Boston College. Graduate School of Arts and Sciences
Discipline: Mathematics
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Champion, Daniel James. "Mobius Structures, Einstein Metrics, and Discrete Conformal Variations on Piecewise Flat Two and Three Dimensional Manifolds." Diss., The University of Arizona, 2011. http://hdl.handle.net/10150/145313.
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Spherical, Euclidean, and hyperbolic simplices can be characterized by the dihedral angles on their codimension-two faces. These characterizations analyze the Gram matrix, a matrix with entries given by cosines of dihedral angles. Hyperideal hyperbolic simplices are non-compact generalizations of hyperbolic simplices wherein the vertices lie outside hyperbolic space. We extend recent characterization results to include fully general hyperideal simplices. Our analysis utilizes the Gram matrix, however we use inversive distances instead of dihedral angles to accommodate fully general hyperideal simplices.For two-dimensional triangulations, an angle structure is an assignment of three face angles to each triangle. An angle structure permits a globally consistent scaling provided the faces can be simultaneously scaled so that any two contiguous faces assign the same length to their common edge. We show that a class of symmetric Euclidean angle structures permits globally consistent scalings. We develop a notion of virtual scaling to accommodate spherical and hyperbolic triangles of differing curvatures and show that a class of symmetric spherical and hyperbolic angle structures permit globally consistent virtual scalings.The double tetrahedron is a triangulation of the three-sphere obtained by gluing two congruent tetrahedra along their boundaries. The pentachoron is a triangulation of the three-sphere obtained from the boundary of the 4-simplex. As piecewise flat manifolds, the geometries of the double tetrahedron and pentachoron are determined by edge lengths that gives rise to a notion of a metric. We study notions of Einstein metrics on the double tetrahedron and pentachoron. Our analysis utilizes Regge's Einstein-Hilbert functional, a piecewise flat analogue of the Einstein-Hilbert (or total scalar curvature) functional on Riemannian manifolds.A notion of conformal structure on a two dimensional piecewise flat manifold is given by a set of edge constants wherein edge lengths are calculated from the edge constants and vertex based parameters. A conformal variation is a smooth one parameter family of the vertex parameters. The analysis of conformal variations often involves the study of degenerating triangles, where a face angle approaches zero. We show for a conformal variation that remains weighted Delaunay, if the conformal parameters are bounded then no triangle degenerations can occur.
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Nguyen, Minh Hoang. "Surfaces minimales dans des variétés homogènes de dimension 3 minimal surfaces in three dimensional homogeneous manifolds." Toulouse 3, 2016. http://www.theses.fr/2016TOU30173.
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Cette thèse est consacrée aux surfaces minimales dans certains espaces homogènes riemanniens de dimension 3. Dans une première partie, nous considérons la variété homogène riemannienne PSL2(IR. , T) qui peut encore être considéré comme IHI2 x IR = {(x, y, z) E JR3 : :r2 + y2 < 4} munie de lametrique. \2 (d:c2 + dy 2) + (x. \(ydx- xdy) + dz) 2 où,\= 4 (oc}+y')" Nous construisons des anneaux plongés complets dont le bord se compose de 4 droites verticales sur le bord à nnfinide IHI2 x IR. . De plus, ces anneaux sont asymptotiques à deux surfaces minimales verticales de PSL2 (1R, T). Ces anneaux sont construits en prenant la limite d'une suite d'anneaux minimaux compacts. L'ingredient principal de cette démonstration est d'estimer la courbure des suites d'anneaux minimaux compacts, basé sur le controle l'espace tangent en utilisant les feuilletages minimaux do PSL2(1R, x). Dans une seconde partie, nous étudions le problème de Dirichlet pour réquation des surfaces minimales dans Sol3 avec des données à bord peut être infinies1 où Sol3 est un groupe de Lie non-abélien résoluble de dimension 3 muni d'une métrique invariante à gauche qui en fait un modèle de l'une des huit géometries de Thurston. Notre résultat est un théorème de type Jenkins-Scrrin qni établit les conditions nécessaires et suffisantes pour l'existence et l'unicité de certains graphes de Killing dans Sol;3, où le champ de vecteur de Killing est non-unitaireThis thesis deals with minimal surfaces in some homogencous Riemannian 3-manifolds. In a first part, we consider the homogeneous Riemannian 3-manifolrl PSL2(1H:, r) which can be vicwed as IHI2 x IR= {(:r,y,z) E IR. 3 : :r2 +y2 < 4} endowcd with the Ricmannian metric>. 2 (dx 2+dy2 )+(r À(ydx- xdy) + dz)2 where À= 4 (x~+y'), we construct complete, embedded minimal annuli whose boundary consists of 4 vertical lines on the boundary at infinity of PSL_2(R, t):. J\. 'forcover, these minimal annuli arc asymptotic ta two vertical minimal surfaces ofPSL2(R r). The annuli arc constructcrl by taldng the limit of a sequence of compact minimalannuli. The main idca of this proof is to cstimatc curvaturc of sequences of compact minimalannuli bascd on controlling their tangent spaccs by using minimal foliations of PSL2 (IR, T). In a second part, \VC study the Dirichlet problem for the minimal surface equation in Sol3\'Vith possible infinite bounda. Ry data, whcrc Sol;~ is the non-Abclian solvable 3-climcnsionalLie group cquippcd \vith its usual !cft-invariant metric that makcs it into a madel spacc forone of the eight Thurston geometries. Our main result is a JcnkinsScrrin type theorcm \Vhichestablishes neccssary and sufficient conditions for the existence and uniqucness of certainminimal Killing graphs \Vith a non-unitary Killing vcctor field in So l3
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Canalias, Vila Elisabet. "Contributions to Libration Orbit Mission Design using Hyperbolic Invariant Manifolds." Doctoral thesis, Universitat Politècnica de Catalunya, 2007. http://hdl.handle.net/10803/5927.
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Aquesta tesi doctoral està emmarcada en el camp de l'astrodinàmica. Presenta solucions a problemes identificats en el disseny de missions que utilitzen òrbites entorn dels punts de libració, fent servir la teoria de sistemes dinàmics.El problema restringit de tres cossos és un model per estudiar el moviment d'un cos de massa infinitessimal sota l'atracció gravitatòria de dos cossos molt massius. Els cinc punts d'equilibri d'aquest model, en especial L1 i L2, han estat motiu de nombrosos estudis per aplicacions pràctiques en les últimes dècades (SOHO, Genesis...).
Genèricament, qualsevol missió en òrbita al voltant del punt L2 del sistema Terra-Sol es veu afectat per ocultacions degudes a l'ombra de la Terra. Si l'òrbita és al voltant de L1, els eclipsis són deguts a la forta influència electromagnètica del Sol. D'entre els diferents tipus d'òrbites de libració, les òrbites de Lissajous resulten de la combinació de dues oscil.lacions perpendiculars. El seu principal avantatge és que les amplituds de les oscil.lacions poden ser escollides independentment i això les fa adapatables als requeriments de cada missió. La necessitat d'estratègies per evitar eclipsis en òrbites de Lissajous entorn dels punts L1 i L2 motivaren la primera part de la tesi. En aquesta part es presenta una eina per la planificació de maniobres en òrbites de Lissajous que no només serveix per solucionar el problema d'evitar els eclipsis, sinó també per trobar trajectòries de transferència entre òrbites d'amplituds diferents i planificar rendez-vous.
Per altra banda, existeixen canals de baix cost que uneixen els punts L1 i L2 d'un sistema donat i representen una manera natural de transferir d'una regió de libració a l'altra. Gràcies al seu caràcter hiperbòlic, una òrbita de libració té uns objectes invariants associats: les varietats estable i inestable. Si tenim present que la varietat estable està formada per trajectòries que tendeixen cap a l'òrbita a la qual estan associades quan el temps avança, i que la varietat inestable fa el mateix però enrera en el temps, una intersecció entre una varietat estable i una d'inestable proporciona un camí asimptòtic entre les òrbites corresponents. Un mètode per trobar connexions d'aquest tipus entre òrbites planes entorn de L1 i L2 es presenta a la segona part de la tesi, i s'hi inclouen els resultats d'aplicar aquest mètode als casos dels problemes restringits Sol Terra i Terra-Lluna.
La idea d'intersecar varietats hiperbòliques es pot aplicar també en la cerca de camins de baix cost entre les regions de libració del sistema Sol-Terra i Terra-Lluna. Si existissin camins naturals de les òrbites de libració solars cap a les lunars, s'obtindria una manera barata d'anar a la Lluna fent servir varietats invariants, cosa que no es pot fer de manera directa. I a l'inversa, un camí de les regions de libració lunars cap a les solars permetria, per exemple, que una estació fos col.locada en òrbita entorn del punt L2 lunar i servís com a base per donar servei a les missions que operen en òrbites de libració del sistema Sol-Terra. A la tercera part de la tesi es presenten mètodes per trobar trajectòries de baix cost que uneixen la regió L2 del sistema Terra-Lluna amb la regió L2 del sistema Sol-Terra, primer per òrbites planes i més endavant per òrbites de Lissajous, fent servir dos problemes de tres cossos acoblats. Un cop trobades les trajectòries en aquest model simplificat, convé refinar-les per fer-les més realistes. Una metodologia per obtenir trajectòries en efemèrides reals JPL a partir de les trobades entre òrbites de Lissajous en el model acoblat es presenta a la part final de la tesi. Aquestes trajectòries necessiten una maniobra en el punt d'acoblament, que és reduïda en el procés de refinat, arribant a obtenir trajectòries de cost zero quan això és possible.
This PhD. thesis lies within the field of astrodynamics. It provides solutions to problems which have been identified in mission design near libration points, by using dynamical systems theory.
The restricted three body problem is a well known model to study the motion of an infinitesimal mass under the gravitational attraction of two massive bodies. Its five equilibrium points, specially L1 and L2, have been the object of several studies aimed at practical applications in the last decades (SOHO, Genesis...).
In general, any mission in orbit around L2 of the Sun-Earth system is affected by occultations due to the shadow of the Earth. When the orbit is around L1, the eclipses are caused by the strong electromagnetic influence of the Sun. Among all different types of libration orbits, Lissajous type ones are the combination of two perpendicular oscillations. Its main advantage is that the amplitudes of the oscillations can be chosen independently and this fact makes Lissajous orbits more adaptable to the requirements of each particular mission than other kinds of libration motions. The need for eclipse avoidance strategies in Lissajous orbits around L1 and L2 motivated the first part of the thesis. It is in this part where a tool for planning maneuvers in Lissajous orbits is presented, which not only solves the eclipse avoidance problem, but can also be used for transferring between orbits having different amplitudes and for planning rendez-vous strategies.
On the other hand, there exist low cost channels joining the L1 and L2 points of a given sistem, which represent a natural way of transferring from one libration region to the other one. Furthermore, there exist hyperbolic invariant objects, called stable and unstable manifolds, which are associated with libration orbits due to their hyperbolic character. If we bear in mind that the stable manifold of a libration orbit consists of trajectories which tend to the orbit as time goes by, and that the unstable manifold does so but backwards in time, any intersection between a stable and an unstable manifold will provide an asymptotic path between the corresponding libration orbits. A methodology for finding such asymptotic connecting paths between planar orbits around L1 and L2 is presented in the second part of the dissertation, including results for the particular cases of the Sun-Earth and Earth-Moon problems.
Moreover, the idea of intersecting hyperbolic manifolds can be applied in the search for low cost paths joining the libration regions of different problems, such as the Sun-Earth and the Earth-Moon ones. If natural paths from the solar libration regions to the lunar ones was found, it would provide a cheap way of transferring to the Moon from the vicinity of the Earth, which is not possible in a direct way using invariant manifolds. And the other way round, paths from the lunar libration regions to the solar ones would allow for the placement of a station in orbit around the lunar L2, providing services to solar libration missions, for instance. In the third part of the thesis, a methodology for finding low cost trajectories joining the lunar L2 region and the solar L2 region is presented. This methodology was developed in a first step for planar orbits and in a further step for Lissajous type orbits, using in both cases two coupled restricted three body problems to model the Sun-Earth-Moon spacecraft four body problem. Once trajectories have been found in this simplified model, it is convenient to refine them to more realistic models. A methodology for obtaining JPL real ephemeris trajectories from the initial ones found in the coupled models is presented in the last part of the dissertation. These trajectories need a maneuver at the coupling point, which can be reduced in the refinement process until low cost connecting trajectories in real ephemeris are obtained (even zero cost, when possible).
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Wheeler, Russell Clark. "Using symbolic dynamical systems: A search for knot invariants." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/3033.
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Mathew, Panakkal J. "Three Topics in Analysis: (I) The Fundamental Theorem of Calculus Implies that of Algebra, (II) Mini Sums for the Riesz Representing Measure, and (III) Holomorphic Domination and Complex Banach Manifolds Similar to Stein Manifolds." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_diss/2.
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We look at three distinct topics in analysis. In the first we give a direct and easy proof that the usual Newton-Leibniz rule implies the fundamental theorem of algebra that any nonconstant complex polynomial of one complex variable has a complex root. Next, we look at the Riesz representation theorem and show that the Riesz representing measure often can be given in the form of mini sums just like in the case of the usual Lebesgue measure on a cube. Lastly, we look at the idea of holomorphic domination and use it to define a class of complex Banach manifolds that is similar in nature and definition to the class of Stein manifolds.
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Deng, Shengfu. "A Spatial Dynamic Approach to Three-Dimensional Gravity-Capillary Water Waves." Diss., Virginia Tech, 2008. http://hdl.handle.net/10919/28254.
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Three-dimensional gravity-capillary steady waves on water of finite-depth, which are uniformly translating in a horizontal propagation direction and periodic in a transverse direction, are considered. The exact Euler equations are formulated as a spatial dynamic system in which the variable used for the propagating direction is the time-like variable. The existence of the solutions of the system is determined by two non-dimensional constants: the Bond number b and λ (the inverse of the square of the Froude number). The property of Sobolev spaces and the spectral analysis show that the spectrum of the linear part consists of isolated eigenvalues of finite algebraic multiplicity and the number of purely imaginary eigenvalues are finite. The distribution of eigenvalues is described by b and λ.
Assume that C1 is the curve in (b,λ)-plane on which the first two eigenvalues for three-dimensional waves collide at the imaginary axis, and that the intersection point of the curve C1 with the line λ=1 is (b0,1) where b0>0. Two cases (b0,1) and (b,λ) â C1 where 0< b< b0 are investigated. A center-manifold reduction technique and a normal form analysis are applied to show that for each case the dynamical system can be reduced to a system of ordinary differential equations with finite dimensions. The dominant system for the case (b0,1) is coupled Schrödinger-KdV equations while it is a Schrödinger equation for another case (b,λ) â C1. Then, from the existence of the homoclinic orbit connecting to the two-dimensional periodic solution (called generalized solitary wave) for the dominant system, it is obtained that such generalized solitary wave solution persists for the original system by using the perturbation method and adjusting some appropriate constants.Ph. D.
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Binotto, Rosane Rossato. "Projetivos de curvatura." [s.n.], 2007. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306624.
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Orientadores: Sueli Irene Rodrigues Costa, Maria del Carmen Romero-FusterTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica
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Resumo: O projetivo de curvatura em um ponto de uma 3-variedade M de classe 'C POT. 2' imersa em 'IR POT. ?' , n >-4, é o lugar geométrico de todos os extremos dos vetores curvatura de secções normais ao longo de todas as direções tangentes a M em p. Mostramos que o projetivo de curvatura em p é isomorfo (difeomorfo) à superfície de Veronese clássica de ordem 2, composta com uma transformação linear. Conforme o posto desta transformação linear, o projetivo de curvatura será dado por projeções da superfície de Veronese em subespaços do espaço normal da variedade M. Quanto menor o posto, maior será a umbilicidade da variedade no ponto em questão. Também estudamos a natureza geométrica e singularidades para os diferentes casos de projetivos de curvatura em pontos de M, os quais incluem a superfície Romana de Steiner, a Cross-Cap, a superfície de Steiner de Tipo 5 e a Cross-Cup. Além disso, analisamos os pontos singulares de segunda ordem da imersão, no sentido de Feldman e estabelecemos condições relacionadas à natureza do projetivo de curvatura, para que uma 3-variedade imersa em 'IR POT. ?', n >_ 9, tenha contato de ordem _ 2 com k-planos e k-esferas de IRn, 3 _ k _ 8
Abstract: The curvature projective plane at each point p of three-manifolds M immersed in 'IR POT. ?', n _ 4, is the geometric locus of all end points of the curvature vectors of normal sections along of all tangent directions of M at p. In this study, we show that the curvature projective plane is isomorphic (diffeomorphic) to the classical Veronese surface of order two, composed with a linear transformation, and that according to the rank of this mapping, the curvature projective plane will be given by projections of the Veronese surface into subspaces of the normal space of M at p. Thus, the smaller the rank the greater the umbilicity of the manifold at this point. We also study the geometric nature and singularities of the curvature projective planes considering different possibilities, which include the Roman Steiner surface, the Cross-Cap, the Steiner surface of five-type, and the Cross-Cup. In addition, we analyze the order-two singularities of the immersion in the Feldman¿s sense and establish conditions related to the nature of the curvature projective plane for the existence of contacts of the three-manifolds in 'IR POT. ?', n _ 9, with k-planes and k-spheres, 3 _ k _ 8
Doutorado
Geometria
Doutor em Matemática
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Cooper, Haydn. "Two generator discrete groups of isometries and their representation : a thesis presented in partial fulfillment of the requirements for the degree of Master of Science in Mathematics at Massey University, Albany, New Zealand." Massey University, 2008. http://hdl.handle.net/10179/973.
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Let M Φ and Mψ be elements of PSL(2,C) representing orientation preserving isometries on the upper half-space model of hyperbolic 3-space Φ and ψ respectively. The parameters β = tr2(M Φ) - 4, β1 = tr2(Mψ) - 4, γ = tr[M Φ,Mψ] - 2, determine the discrete group (Φ ,ψ) uniquely up to conjugacy whenever γ ≠ 0. This thesis is concerned with explicitly lifting this parameterisation of (Φ , ψ) to PSO(1, 3) realised as a discrete 2 generator subgroup of orientation preserving isometries on the hyperboloid model of hyperbolic 3-space. We particularly focus on the case where both Φ and ψ are elliptic.
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Zhu, Xueyun. "Vlist and Ering: compact data structures for simplicial 2-complexes." Thesis, Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/50389.
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Various data structures have been proposed for representing the connectivity of manifold triangle meshes. For example, the Extended Corner Table (ECT) stores V+6T references, where V and T respectively denote the vertex and triangle counts. ECT supports Random Access and Traversal (RAT) operators at Constant Amortized Time (CAT) cost. We propose two novel variations of ECT that also support RAT operations at CAT cost, but can be used to represent and process Simplicial 2-Complexes (S2Cs), which may represent star-connecting, non-orientable, and non-manifold triangulations along with dangling edges, which we call sticks. Vlist stores V+3T+3S+3(C+S-N) references, where S denotes the stick count, C denotes the number of edge-connected components and N denotes the number of star-connecting vertices. Ering stores 6T+3S+3(C+S-N) references, but has two advantages over Vlist: the Ering implementation of the operators is faster and is purely topological (i.e., it does not perform geometric queries). Vlist and Ering representations have two principal advantages over previously proposed representations for simplicial complexes: (1) Lower storage cost, at least for meshes with significantly more triangles than sticks, and (2) explicit support of side-respecting traversal operators which each walks from a corner on the face of a triangle t across an edge or a vertex of t, to a corner on a faces of a triangle or to an end of a stick that share a vertex with t, and this without ever piercing through the surface of a triangle.
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Sun, Jian. "Reconstructing and analyzing surfaces in 3-space." Columbus, Ohio : Ohio State University, 2007. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1184337519.
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Alcântara, Marcos Aurélio de. "Rigidez de superfícies convexas em espaços homogêneos 3-dimensionais." Universidade Federal do Amazonas, 2013. http://tede.ufam.edu.br/handle/tede/3671.
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This paper presents main result of a theorem in rigidity of convex three dimensional homogeneous spaces, which was proved by Hosenberg and Tribuzy in 2011. More precisely, we prove that given smooth family of isometric immersions strictly convex f(t) : M ! N, with f(0) = f, Ke(ft(x)) = Ke(f(x)) for x 2 M and for all t, and H(ft(x)) = H(f(x)) in three distinct points x of M. Then there are isometries h(t) : N ! N such that h(t)f(t) = f.
Este trabalho apresenta como principal resultado um teorema de rigidez de superfícies convexas em espaços homogêneos tridimensionais, que foi provado por Hosenberg e Tribuzy em 2011. Mais precisamente, provaremos que dada uma família suave de imersões isométricas estritamente convexa f(t) : M ! N, com f(0) = f, Ke(ft(x)) = Ke(f(x)) para x 2 M e todo t, e H(ft(x)) = H(f(x)) em três pontos distintos x de M. Então existem isometrias h(t) : N ! N tal que h(t)f(t) = f.
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Masdemont, Soler Josep. "Estudi i utilització de materials invariants en problemes de mecànica celeste." Doctoral thesis, Universitat Politècnica de Catalunya, 1991. http://hdl.handle.net/10803/6713.
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La memòria consta de dues parts. En la primera d'elles s'estudien les òrbites homoclíniques i heteroclíniques associades als punts d'equilibri triangulars del problema restringit circular i pla per valors del paràmetre de masses compresos entre 0.1 i 0.5, es donen resultats referents a la seva forma i nombre. En la segona part òrbita halo al voltant del punt l1 del sistema terra-sol, utilitzant les idees geomètriques que proporciona la teoria dels sistemes dinàmics. Es comença l'estudi per models senzills a fi de veure l'essencial de la geometria del problema i la influencia de la lluna, per finalitzar utilitzant el model de sistema solar real donat per les efemèrides del JPL.
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Weiner, Ian. "Super-Symmetric Three-Cycles in String Theory." Scholarship @ Claremont, 2001. https://scholarship.claremont.edu/hmc_theses/138.
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We determine several families of so-called associative 3-dimensional manifolds in R7. Such manifolds are of interest because associative 3-cycles in G2 holonomy manifolds such as R6 × S1, whose universal cover is R7, are candidates for representations of fundamental particles in String Theory. We apply the classic results of Harvey and Lawson to find 3-manifolds which are graphs of functions f : Im H → H and which are invariant under a particular 1-parameter subgroup of G2, the automorphism group of the Cayley numbers, O. Systems of PDEs are derived and solved, some special cases of a classic theorem of Harvey and Lawson are investigated, and theorems aiding in the classification of all such manifolds described here are proven. It is found that in most of the cases examined, the resulting manifold must be of the form of the graph of a holomorphic function crossed with R. However, some examples of other types of graphs are also found.
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"Three dimensional contact topology." 2013. http://library.cuhk.edu.hk/record=b5884528.
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Low, Ho Chi.Thesis (M.Phil.)--Chinese University of Hong Kong, 2013.
Includes bibliographical references (leaves 76-79).
Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web.
Abstracts also in Chinese.
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Leininger, Christopher Jay. "Essential surfaces in hyperbolic three-manifolds." 2002. http://wwwlib.umi.com/cr/utexas/fullcit?p3114769.
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Derby-Talbot, Ryan. "Heegaard splittings of toroidal 3-manifolds." Thesis, 2006. http://hdl.handle.net/2152/2517.
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Chesebro, Eric Bruce. "Undetected boundary slopes and roots of unity for the character variety of a 3-manifold." Thesis, 2006. http://hdl.handle.net/2152/2475.
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Goodman, Noah Daniel. "Contact structures and open books." Thesis, 2003. http://wwwlib.umi.com/cr/utexas/fullcit?p3116314.
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Przeworski, Andrew. "Tubes in hyperbolic 3-manifolds /." 2000. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:9965140.
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"Margulis number for hyperbolic 3-manifolds." 2011. http://library.cuhk.edu.hk/record=b5894652.
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Yiu, Fa Wai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2011.
Includes bibliographical references (leaves 55-58).
Abstracts in English and Chinese.
Chapter 1 --- Introduction --- p.6
Chapter 2 --- Elementary properties and notations of Hyperbolic space --- p.9
Chapter 3 --- Poisson kernel and Conformal densities --- p.16
Chapter 3.1 --- Poisson kernel --- p.17
Chapter 3.2 --- Conformal densities --- p.19
Chapter 4 --- Patterson construction and decomposition --- p.27
Chapter 4.1 --- Patterson construction --- p.27
Chapter 4.2 --- Patterson decomposition --- p.33
Chapter 5 --- Bonahon surfaces and Grided surfaces --- p.39
Chapter 5.1 --- Bonahon surfaces --- p.40
Chapter 5.2 --- Grided surfaces --- p.46
Chapter 6 --- Margulis number of Hyperbolic Manifolds --- p.51
Margulis Number for Hypcrbolic 3-manifolds --- p.5
Chapter 6.1 --- Gcomertrically finite groups --- p.51
Chapter 6.2 --- Margulis number of Closed Hyperbolic Manifolds --- p.53
Bibliography --- p.55
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Arıkan, Mehmet Fırat. "Topological invariants of contact structures and planar open books." Diss., 2008.
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Schlatter, Emma Louise. "Knot theory and applications to 3-manifolds." 2010. http://hdl.handle.net/10090/15209.
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Jones, Kerry Nelson. "Cone manifolds in three-dimensional topology applications to branched covers." Thesis, 1990. http://hdl.handle.net/1911/16355.
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Cone manifolds are defined and several standard geometric techniques for Riemannian manifolds are generalized to this setting.
Smoothing techniques for approximating cone manifolds by smooth Riemannian manifolds with bounded sectional curvature are discussed. This involves some quite explicit curvature computations.
The connection is then made between branched covers and cone manifolds by showing that cone manifold structures lift to a branched cover. Topological results concerning existence of incompressible tori and Seifert-fibered spaces in branched covers are then obtained by lifting cone manifold structures to a branched cover, smoothing the cone manifold structure to a bounded curvature metric, then using differential-geometric techniques on the smooth manifold.
These results are then used in several explicit examples.
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Kao, Wei-Ting, and 高尉庭. "The variation of p-mass on three dimensional CR manifolds." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/u8s2e9.
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碩士國立臺灣大學
數學研究所
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We consider a family of pseudohermitian manifolds in two dimensional complex vector space, described by the level sets of a defining function, and give the variation formula of p-mass for this deformation. To obtain this result, we generalize the ambient connection done by Graham and Lee for arbitrary contact form and derive the conformal transformation in this theory.