Gotowe bibliografie tematyczne / Metric geometry of singularities

Spis treści

  1. Artykuły w czasopismach
  2. Rozprawy doktorskie
  3. Książki
  4. Części książek
  5. Streszczenia konferencji

Gotowa bibliografia na temat „Metric geometry of singularities”

Autor: Grafiati
Data publikacji: 1 września 2023

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Artykuły w czasopismach na temat "Metric geometry of singularities"

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Sabourau, Stéphane, and Zeina Yassine. "A systolic-like extremal genus two surface." Journal of Topology and Analysis 11, no. 03 (2019): 721–38. http://dx.doi.org/10.1142/s1793525319500298.

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It is known that the genus two surface admits a piecewise flat metric with conical singularities which is extremal for the systolic inequality among all nonpositively curved metrics. We prove that this piecewise flat metric is also critical for slow metric variations, without curvature restrictions, for another type of systolic inequality involving the lengths of the shortest noncontractible loops in different free homotopy classes.
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Stoica, Ovidiu-Cristinel. "Spacetimes with singularities." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 2 (2012): 213–38. http://dx.doi.org/10.2478/v10309-012-0050-3.

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Abstract We report on some advances made in the problem of singularities in general relativity.First is introduced the singular semi-Riemannian geometry for metrics which can change their signature (in particular be degenerate). The standard operations like covariant contraction, covariant derivative, and constructions like the Riemann curvature are usually prohibited by the fact that the metric is not invertible. The things become even worse at the points where the signature changes. We show that we can still do many of these operations, in a different framework which we propose. This allows
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Li, Chi. "On the limit behavior of metrics in the continuity method for the Kähler–Einstein problem on a toric Fano manifold." Compositio Mathematica 148, no. 6 (2012): 1985–2003. http://dx.doi.org/10.1112/s0010437x12000334.

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AbstractThis work is a continuation of the author’s previous paper [Greatest lower bounds on the Ricci curvature of toric Fano manifolds, Adv. Math. 226 (2011), 4921–4932]. On any toric Fano manifold, we discuss the behavior of the limit metric of a sequence of metrics which are solutions to a continuity family of complex Monge–Ampère equations in the Kähler–Einstein problem. We show that the limit metric satisfies a singular complex Monge–Ampère equation. This gives a conic-type singularity for the limit metric. Information on conic-type singularities can be read off from the geometry of the
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García Ariza, M. Á. "Degenerate Hessian structures on radiant manifolds." International Journal of Geometric Methods in Modern Physics 15, no. 06 (2018): 1850087. http://dx.doi.org/10.1142/s0219887818500871.

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We present a rigorous mathematical treatment of Ruppeiner geometry, by considering degenerate Hessian metrics defined on radiant manifolds. A manifold [Formula: see text] is said to be radiant if it is endowed with a symmetric, flat connection and a global vector field [Formula: see text] whose covariant derivative is the identity mapping. A degenerate Hessian metric on [Formula: see text] is a degenerate metric tensor that can locally be written as the covariant Hessian of a function, called potential. A function on [Formula: see text] is said to be extensive if its Lie derivative with respec
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Birbrair, Lev, and Alexandre Fernandes. "Inner metric geometry of complex algebraic surfaces with isolated singularities." Communications on Pure and Applied Mathematics 61, no. 11 (2008): 1483–94. http://dx.doi.org/10.1002/cpa.20244.

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LUO, FENG. "COMBINATORIAL YAMABE FLOW ON SURFACES." Communications in Contemporary Mathematics 06, no. 05 (2004): 765–80. http://dx.doi.org/10.1142/s0219199704001501.

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In this paper we develop an approach to conformal geometry of piecewise flat metrics on manifolds. In particular, we formulate the combinatorial Yamabe problem for piecewise flat metrics. In the case of surfaces, we define the combinatorial Yamabe flow on the space of all piecewise flat metrics associated to a triangulated surface. We show that the flow either develops removable singularities or converges exponentially fast to a constant combinatorial curvature metric. If the singularity develops, we show that the singularity is always removable by a surgery procedure on the triangulation. We
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Botvinnik, Boris. "Manifolds with singularities accepting a metric of positive scalar curvature." Geometry & Topology 5, no. 2 (2001): 683–718. http://dx.doi.org/10.2140/gt.2001.5.683.

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Larrañaga, Alexis, Natalia Herrera, and Juliana Garcia. "Geometric Description of the Thermodynamics of the Noncommutative Schwarzschild Black Hole." Advances in High Energy Physics 2013 (2013): 1–6. http://dx.doi.org/10.1155/2013/641273.

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The thermodynamics of the noncommutative Schwarzschild black hole is reformulated within the context of the recently developed formalism of geometrothermodynamics (GTD). Using a thermodynamic metric which is invariant with respect to Legendre transformations, we determine the geometry of the space of equilibrium states and show that phase transitions, which correspond to divergencies of the heat capacity, are represented geometrically as singularities of the curvature scalar. This further indicates that the curvature of the thermodynamic metric is a measure of thermodynamic interaction.
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Ashtekar, Abhay, and Javier Olmedo. "Properties of a recent quantum extension of the Kruskal geometry." International Journal of Modern Physics D 29, no. 10 (2020): 2050076. http://dx.doi.org/10.1142/s0218271820500765.

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Recently, it was shown that, in an effective description motivated by loop quantum gravity, singularities of the Kruskal spacetime are naturally resolved [A. Ashtekar, J. Olmedo and P. Singh, Phys. Rev. Lett. 121 (2018) 241301; A. Ashtekar, J. Olmedo and P. Singh, Phys. Rev. D 98 (2018) 126003]. In this paper, we explore a few properties of this quantum corrected effective metric. In particular, we (i) calculate the Hawking temperature associated with the horizon of the effective geometry and show that the quantum correction to the temperature is completely negligible for macroscopic black hol
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Han, Yiwen, and XiaoXiong Zeng. "Legendre Invariance and Geometrothermodynamics Description of the 3D Charged-Dilaton Black Hole." Advances in High Energy Physics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/865354.

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We first review Weinhold information geometry and Ruppeiner information geometry of 3D charged-dilaton black hole. Then, we use the Legendre invariant to introduce a 2-dimensional thermodynamic metric in the space of equilibrium states, which becomes singular at those points. According to the analysis of the heat capacities, these points are the places where phase transitions occur. This result is valid for the black hole, therefore, provides a geometrothermodynamics description of black hole phase transitions in terms of curvature singularities.
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Rozprawy doktorskie na temat "Metric geometry of singularities"

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Oudrane, M'hammed. "Projections régulières, structure de Lipschitz des ensembles définissables et faisceaux de Sobolev." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4034.

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Dans cette thèse, nous abordons des questions autour de la structure métrique des ensembles définissables dans les structures o-minimales.Dans la première partie, nous étudions les projections régulières au sens de Mostowski, nous prouvons que ces projections n'existent que pour les structures polynomialement bornées, nous utilisons les projections régulières pour refaire la preuve de Parusinski de l'existence des recouvrements réguliers. Dans la deuxième partie de cette thèse, nous étudions les faisceaux de Sobolev (au sens de Lebeau). Pour les fonctions de Sobolev de régularité entière posit
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Lebl, Jiří́. "Singularities and Complexity in CR Geometry." Connect to a 24 p. preview or request complete full text in PDF format. Access restricted to UC campuses, 2007. http://wwwlib.umi.com/cr/ucsd/fullcit?p3254327.

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Thesis (Ph. D.)--University of California, San Diego, 2007.<br>Title from first page of PDF file (viewed May 2, 2007). Available via ProQuest Digital Dissertations. Vita. Includes bibliographical references (p. 101-104).
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Ronaldson, Luke James. "The geometry of weak gravitational singularities." Thesis, University of Southampton, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.485292.

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Coffey, Michael R. "Ricci flow and metric geometry." Thesis, University of Warwick, 2015. http://wrap.warwick.ac.uk/67924/.

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This thesis considers two separate problems in the field of Ricci flow on surfaces. Firstly, we examine the situation of the Ricci flow on Alexandrov surfaces, which are a class of metric spaces equipped with a notion of curvature. We extend the existence and uniqueness results of Thomas Richard in the closed case to the setting of non-compact Alexandrov surfaces that are uniformly non-collapsed. We complement these results with an extensive survey that collects together, for the first time, the essential topics in the metric geometry of Alexandrov spaces due to a variety of authors. Secondly,
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van, Staden Wernd Jakobus. "Metric aspects of noncommutative geometry." Diss., University of Pretoria, 2019. http://hdl.handle.net/2263/77893.

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We study noncommutative geometry from a metric point of view by constructing examples of spectral triples and explicitly calculating Connes's spectral distance between certain associated pure states. After considering instructive nite-dimensional spectral triples, the noncommutative geometry of the in nite-dimensional Moyal plane is studied. The corresponding spectral triple is based on the Moyal deformation of the algebra of Schwartz functions on the Euclidean plane.<br>Dissertation (MSc)--University of Pretoria, 2019.<br>Physics<br>MSc<br>Unrestricted
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Mangalath, Vishnu. "Singularities of Whitham Deformations." Thesis, The University of Sydney, 2021. https://hdl.handle.net/2123/25990.

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Constant mean curvature planes of finite type in Euclidean 3-space are in correspondence with spectral data, consisting of a hyperelliptic (spectral) curve, two meromorphic differentials, and a line bundle. A class of deformations one can consider are known as Whitham or period preserving deformations. Singularities of Whitham deformations can occur if the differentials have common roots on the spectral curve. In this thesis we are concerned with studying deformations within, and out of, the space of spectral data at which the Whitham equations are singular. We show in a special case that sing
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Palmer, Ian Christian. "Riemannian geometry of compact metric spaces." Diss., Georgia Institute of Technology, 2010. http://hdl.handle.net/1853/34744.

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A construction is given for which the Hausdorff measure and dimension of an arbitrary abstract compact metric space (X, d) can be encoded in a spectral triple. By introducing the concept of resolving sequence of open covers, conditions are given under which the topology, metric, and Hausdorff measure can be recovered from a spectral triple dependent on such a sequence. The construction holds for arbitrary compact metric spaces, generalizing previous results for fractals, as well as the original setting of manifolds, and also holds when Hausdorff and box dimensions differ---in particular, it does n
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Jägrell, Linus. "Geometry of the Lunin-Maldacena metric." Thesis, KTH, Teoretisk fysik, 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-153502.

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Milicevic, Luka. "Topics in metric geometry, combinatorial geometry, extremal combinatorics and additive combinatorics." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273375.

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Persson, Nicklas. "Shortest paths and geodesics in metric spaces." Thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-66732.

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This thesis is divided into three part, the first part concerns metric spaces and specically length spaces where the existence of shortest path between points is the main focus. In the second part, an example of a length space, the Riemannian geometry will be given. Here both a classical approach to Riemannian geometry will be given together with specic results when considered as a metric space. In the third part, the Finsler geometry will be examined both with a classical approach and trying to deal with it as a metric space.
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Książki na temat "Metric geometry of singularities"

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López, Antonio Campillo, and Luis Narváez Macarro, eds. Algebraic Geometry and Singularities. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9020-5.

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1953-, Campillo Antonio, Narváez Macarro Luis 1957-, and International Conference on Algebraic Geometry (3rd : 1991 : Rábida (Monastery)), eds. Algebraic geometry and singularities. Birkhäuser Verlag, 1995.

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Snapper, Ernst. Metric affine geometry. Dover Publications, 1989.

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G, Paré E., ed. Descriptive geometry: Metric. 7th ed. Macmillan, 1987.

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Libgober, Anatoly. Trends in Singularities. Birkhäuser Basel, 2002.

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Blanlœil, Vincent, and Toru Ohmoto, eds. Singularities in Geometry and Topology. European Mathematical Society Publishing House, 2012. http://dx.doi.org/10.4171/118.

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Dai, Xianzhe, and Xiaochun Rong, eds. Metric and Differential Geometry. Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0257-4.

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Metric and comparison geometry. International Press, 2007.

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Melles, Caroline Grant, and Ruth I. Michler, eds. Singularities in Algebraic and Analytic Geometry. American Mathematical Society, 2000. http://dx.doi.org/10.1090/conm/266.

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Neumann, Walter, and Anne Pichon, eds. Introduction to Lipschitz Geometry of Singularities. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-61807-0.

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Części książek na temat "Metric geometry of singularities"

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Ruano, Diego. "The Metric Structure of Linear Codes." In Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-96827-8_24.

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Burago, Yuri, and David Shoenthal. "Metric Geometry." In New Analytic and Geometric Methods in Inverse Problems. Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-662-08966-8_1.

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Cambanis, Stamatis, and Donald Richards. "Metric geometry." In I.J. Schoenberg Selected Papers. Birkhäuser Boston, 1988. http://dx.doi.org/10.1007/978-1-4612-3948-2_15.

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de Jong, Theo, and Gerhard Pfister. "Deformations of Singularities." In Local Analytic Geometry. Vieweg+Teubner Verlag, 2000. http://dx.doi.org/10.1007/978-3-322-90159-0_10.

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de Jong, Theo, and Gerhard Pfister. "Plane Curve Singularities." In Local Analytic Geometry. Vieweg+Teubner Verlag, 2000. http://dx.doi.org/10.1007/978-3-322-90159-0_5.

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Millman, Richard S., and George D. Parker. "Incidence and Metric Geometry." In Geometry. Springer New York, 1991. http://dx.doi.org/10.1007/978-1-4612-4436-3_2.

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Bădescu, Lucian. "Quasi-homogeneous Singularities and Projective Geometry." In Projective Geometry and Formal Geometry. Birkhäuser Basel, 2004. http://dx.doi.org/10.1007/978-3-0348-7936-1_5.

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Brasselet, Jean-Paul. "Singularities and Noncommutative Geometry." In New Developments in Singularity Theory. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0834-1_6.

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Pop, Florian. "Alterations and Birational Anabelian Geometry." In Resolution of Singularities. Birkhäuser Basel, 2000. http://dx.doi.org/10.1007/978-3-0348-8399-3_19.

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Hofer, Helmut, Alberto Abbondandolo, Urs Frauenfelder, and Felix Schlenk. "Lagrangian skeleta and plane curve singularities." In Symplectic Geometry. Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-19111-4_9.

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Streszczenia konferencji na temat "Metric geometry of singularities"

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BIRBRAIR, L. "METRIC THEORY OF SINGULARITIES: LIPSCHITZ GEOMETRY OF SINGULAR SPACES." In Proceedings of the Trieste Singularity Summer School and Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812706812_0006.

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Ghosal, Ashitava, and Bahram Ravani. "Differential Geometric Analysis of Singularities of Point Trajectories of Serial and Parallel Manipulators." In ASME 1998 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1998. http://dx.doi.org/10.1115/detc98/mech-5967.

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Abstract In this paper, we present a differential-geometric analysis of singularities of point trajectories of two and three-degree-of-freedom serial and parallel manipulators. At non-singular configurations, the first order local properties are characterized by the metric coefficients, and, geometrically, by the shape and size of a velocity ellipse and ellipsoid for two and three-degree-of-freedom motions respectively. At singular configurations, the definition of a metric is no longer valid and the velocity ellipsoid degenerates to an ellipse, a line or a point, and the area or the volume of
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VERBITSKY, MISHA. "SINGULARITIES IN HYPERKÄHLER GEOMETRY." In Proceedings of the Second Meeting. WORLD SCIENTIFIC, 2001. http://dx.doi.org/10.1142/9789812810038_0029.

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Chaperon, Marc. "Singularities in contact geometry." In Geometry and Topology of Caustics – Caustics '02. Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc62-0-3.

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Goryunov, Victor, and Gabor Lippner. "Simple framed curve singularities." In Geometry and topology of caustics. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc82-0-6.

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Fukuda, Takuo, and Stanisław Janeczko. "On singularities of Hamiltonian mappings." In Geometry and topology of caustics. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc82-0-4.

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Berry, M. V. "WAVE GEOMETRY: A PLURALITY OF SINGULARITIES." In Proceedings of the International Conference on Fundamental Aspects of Quantum Theory — to Celebrate 30 Years of the Aharonov-Bohm-Effect. WORLD SCIENTIFIC, 1991. http://dx.doi.org/10.1142/9789814439251_0008.

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Joets, Alain. "Singularities in drawings of singular surfaces." In Geometry and topology of caustics. Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc82-0-10.

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Lu, Zhengdong, Prateek Jain, and Inderjit S. Dhillon. "Geometry-aware metric learning." In the 26th Annual International Conference. ACM Press, 2009. http://dx.doi.org/10.1145/1553374.1553461.

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Ribotta, Roland, Ahmed Belaidi, and Alain Joets. "Singularities, defects and chaos in organized fluids." In Geometry and Topology of Caustics – Caustics '02. Institute of Mathematics Polish Academy of Sciences, 2003. http://dx.doi.org/10.4064/bc62-0-17.

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