Relevant bibliographies by topics / Hyperbolicity theory

Academic literature on the topic 'Hyperbolicity theory'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Hyperbolicity theory"

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Campana, Frédéric, Lionel Darondeau, and Erwan Rousseau. "Orbifold hyperbolicity." Compositio Mathematica 156, no. 8 (August 2020): 1664–98. http://dx.doi.org/10.1112/s0010437x20007265.

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AbstractWe define and study jet bundles in the geometric orbifold category. We show that the usual arguments from the compact and the logarithmic settings do not all extend to this more general framework. This is illustrated by simple examples of orbifold pairs of general type that do not admit any global jet differential, even if some of these examples satisfy the Green–Griffiths–Lang conjecture. This contrasts with an important result of Demailly (Holomorphic Morse inequalities and the Green-Griffiths-Lang conjecture, Pure Appl. Math. Q. 7 (2011), 1165–1207) proving that compact varieties of general type always admit jet differentials. We illustrate the usefulness of the study of orbifold jets by establishing the hyperbolicity of some orbifold surfaces, that cannot be derived from the current techniques in Nevanlinna theory. We also conjecture that Demailly's theorem should hold for orbifold pairs with smooth boundary divisors under a certain natural multiplicity condition, and provide some evidence towards it.
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Gromov, M. "Kähler hyperbolicity and $L_2$-Hodge theory." Journal of Differential Geometry 33, no. 1 (1991): 263–92. http://dx.doi.org/10.4310/jdg/1214446039.

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Adams, Colin, Or Eisenberg, Jonah Greenberg, Kabir Kapoor, Zhen Liang, Kate O’Connor, Natalia Pacheco-Tallaj, and Yi Wang. "TG-Hyperbolicity of virtual links." Journal of Knot Theory and Its Ramifications 28, no. 12 (October 2019): 1950080. http://dx.doi.org/10.1142/s0218216519500809.

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We extend the theory of hyperbolicity of links in the 3-sphere to tg-hyperbolicity of virtual links, using the fact that the theory of virtual links can be translated into the theory of links living in closed orientable thickened surfaces. When the boundary surfaces are taken to be totally geodesic, we obtain a tg-hyperbolic structure with a unique associated volume. We prove that all virtual alternating links are tg-hyperbolic. We further extend tg-hyperbolicity to several classes of non-alternating virtual links. We then consider bounds on volumes of virtual links and include a table for volumes of the 116 nontrivial virtual knots of four or fewer crossings, all of which, with the exception of the trefoil knot, turn out to be tg-hyperbolic.
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Portilla, Ana, José M. Rodríguez, José M. Sigarreta, and Eva Tourís. "Gromov Hyperbolicity in Directed Graphs." Symmetry 12, no. 1 (January 6, 2020): 105. http://dx.doi.org/10.3390/sym12010105.

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In this paper, we generalize the classical definition of Gromov hyperbolicity to the context of directed graphs and we extend one of the main results of the theory: the equivalence of the Gromov hyperbolicity and the geodesic stability. This theorem has potential applications to the development of solutions for secure data transfer on the internet.
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Riaza, Ricardo, and Caren Tischendorf. "The hyperbolicity problem in electrical circuit theory." Mathematical Methods in the Applied Sciences 33, no. 17 (November 21, 2010): 2037–49. http://dx.doi.org/10.1002/mma.1312.

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Iwaki, E., S. O. Juriaans, and A. C. Souza Filho. "Hyperbolicity of semigroup algebras." Journal of Algebra 319, no. 12 (June 2008): 5000–5015. http://dx.doi.org/10.1016/j.jalgebra.2008.03.015.

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Stewart, Andrew L., and Paul J. Dellar. "Multilayer shallow water equations with complete Coriolis force. Part 3. Hyperbolicity and stability under shear." Journal of Fluid Mechanics 723 (April 16, 2013): 289–317. http://dx.doi.org/10.1017/jfm.2013.121.

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AbstractWe analyse the hyperbolicity of our multilayer shallow water equations that include the complete Coriolis force due to the Earth’s rotation. Shallow water theory represents flows in which the vertical shear is concentrated into vortex sheets between layers of uniform velocity. Such configurations are subject to Kelvin–Helmholtz instabilities, with arbitrarily large growth rates for sufficiently short-wavelength disturbances. These instabilities manifest themselves through a loss of hyperbolicity in the shallow water equations, rendering them ill-posed for the solution of initial value problems. We show that, in the limit of vanishingly small density difference between the two layers, our two-layer shallow water equations remain hyperbolic when the velocity difference remains below the same threshold that also ensures the hyperbolicity of the standard shallow water equations. Direct calculation of the domain of hyperbolicity becomes much less tractable for three or more layers, so we demonstrate numerically that the threshold for the velocity differences, below which the three-layer equations remain hyperbolic, is also unchanged by the inclusion of the complete Coriolis force. In all cases, the shape of the domain of hyperbolicity, which extends outside the threshold, changes considerably. The standard shallow water equations only lose hyperbolicity due to shear parallel to the direction of wave propagation, but the complete Coriolis force introduces another mechanism for loss of hyperbolicity due to shear in the perpendicular direction. We demonstrate that this additional mechanism corresponds to the onset of a transverse shear instability driven by the non-traditional components of the Coriolis force in a three-dimensional continuously stratified fluid.
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Boyde, Guy. "p-Hyperbolicity of homotopy groups via K-theory." Mathematische Zeitschrift 301, no. 1 (January 7, 2022): 977–1009. http://dx.doi.org/10.1007/s00209-021-02917-1.

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AbstractWe show that $$S^n \vee S^m$$ S n ∨ S m is $${\mathbb {Z}}/p^r$$ Z / p r -hyperbolic for all primes p and all $$r \in {\mathbb {Z}}^+$$ r ∈ Z + , provided $$n,m \ge 2$$ n , m ≥ 2 , and consequently that various spaces containing $$S^n \vee S^m$$ S n ∨ S m as a p-local retract are $${\mathbb {Z}}/p^r$$ Z / p r -hyperbolic. We then give a K-theory criterion for a suspension $$\Sigma X$$ Σ X to be p-hyperbolic, and use it to deduce that the suspension of a complex Grassmannian $$\Sigma Gr_{k,n}$$ Σ G r k , n is p-hyperbolic for all odd primes p when $$n \ge 3$$ n ≥ 3 and $$0<k<n$$ 0 < k < n . We obtain similar results for some related spaces.
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Barreira, Luis, and Claudia Valls. "Spectral theory for invertible cocycles under nonuniform hyperbolicity." São Paulo Journal of Mathematical Sciences 12, no. 1 (August 11, 2017): 6–17. http://dx.doi.org/10.1007/s40863-017-0070-z.

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Bermudo, Sergio, José M. Rodríguez, and José M. Sigarreta. "Computing the hyperbolicity constant." Computers & Mathematics with Applications 62, no. 12 (December 2011): 4592–95. http://dx.doi.org/10.1016/j.camwa.2011.10.041.

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Dissertations / Theses on the topic "Hyperbolicity theory"

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Bubani, Elia. "Homeomorphic extension of Quasi-Isometries and Iteration Theory." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23243/.

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Starting from the Riemann Mapping Theorem it arises the interest for biholomorphisms over domains in one or several complex variables. Poincar´e showed that there is no analytic isomorphism between the Polydisc and the unit ball already in C^2. The previous fact may suggest that biholomorphic domains are a class of such well-behaved sets that could extend some regularity of the biholomorpshism until their respective boundaries. A very influent approach was faced by Fefferman (published in the year 1974), by proving that every biholomorphism between bounded strongly pseudoconvex domains with smooth boundaries extends as a diffeomorphism to the closures of the domains. In this work is quoted a classical result that presents an isometry respect to the Bergman metric between biholomorphic domains and he noticed an interesting behaviour of geodesics when they are going to the boundary of a considered domain. The first part of this thesis mainly follows Abate’s work aiming to show the homeomorphic extension of a biholomorphism between C^2-smooth strongly pseudoconvex domains. The second part of this thesis mainly follows the work of Bracci, Gaussier and Zimmer aiming to show the homeomorphic extension of a Quasi-Isometric homeomorphisms to the End compactifications of the respective domains. Other consequences are related to extend the Denjoy-Wolff Theorem for domains in several complex variables and present the Denjoy-Wolff behaviour for commuting holomorphic selfmaps with no fixed point in the domain itself.
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Nicol, Andrew. "Quasi-isometries of graph manifolds do not preserve non-positive curvature." The Ohio State University, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=osu1405894640.

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Rodriguez, Vazquez Rita. "A non-Archimedean Montel's theorem." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX027/document.

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Cette thèse est dédiée à l'étude des propriétés de compacité de familles d'applications analytiques entre espaces analytiques définis sur un corps métrisé non-Archimédien $k$.Nous travaillons dans le contexte des espaces analytiques développés par Berkovich pour exploiter leur topologie modérée.Une de nos motivations est le désire d'introduire une notion naturelle d'hyperbolicité au sens de Kobayashi dans ce cadre.Nous démontrons d'abord un analogue au théorème de Montel pour des applications analytiques à valeurs dans un domaine borné de l'espace affine.Afin de ceci faire, nous paramétrisons l'espace des applications analytiques d'un polydisque ouvert dans un polydique fermé par le spectre analytique d'une $k$-algèbre de Banach adéquate.Le résultat découle alors de la compacité séquentielle de cet espace.Nos résultats mènent naturellement à une définition de famille normale, et nous introduisons ensuite deux ensembles de Fatou associés à un endomorphisme de l'espace projectif.Nous montrons que les composantes de Fatou se comportent comme dans le cas complexeet ne contiennent pas d'image non-triviale de la droite affine épointée.Ensuite, nous appliquons notre notion de normalité à l'étude de l'hyperbolicité dans le cadre non-Archimédien.Nous reprenons les travaux de W. Cherry et démontrons plusieurs caractérisations des variétés projectives lisses pour lesquelles la semi-distance de Cherry-Kobayashi sur l'ensemble des points rigides définit la topologie usuelle.Nous obtenons finalement une caractérisation des courbes algébriques lisses $X$ de caractéristique d'Euler négative en termes de la normalité de certaines familles d'applications analytiques à valeurs dans $X$
This thesis is devoted to the study of compactness properties of spaces of analytic maps between analytic spaces defined over a non-Archimedean metrized field $k$. We work in the theory of analytic spaces as developed by Berkovich to fully exploit their tame topology. One of our motivations is the strive to introduce a natural notion of Kobayashi hyperbolicity in this setting.We first prove an analogue of Montel’s theorem for analytic maps taking values in a bounded domain of the affine space. In order to do so, we parametrize the space of analytic maps from an open polydisk to a closed one by the analytic spectrum of a suitable Banach $k$-algebra. Our result then follows from the sequential compactness of this space.Our results naturally lead to a definition of normal families, and we subsequently introduce two notions of Fatou sets attached to an endomorphism of the projective space. We show that Fatou components behave like in the complex case and cannot contain non trivial images of the punctured affine line.Thereupon, we apply our normality notion to the study of hyperbolicity in the non-Archimedean setting. We pursue the work of W. Cherry and prove various characterizations of smooth projective varieties whose Cherry-Kobayashi semi distance on the set of rigid points defines the classical topology. We finally obtain a characterization of smooth algebraic curves $X$ of negative Euler characteristic in terms of the normality of certain families of analytic maps taking values in $X$
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Canestrari, Giovanni. "On the Kolmogorov property of a class of infinite measure hyperbolic dynamical systems." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/22352/.

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Smooth maps with singularities describe important physical phenomena such as the collisions of rigid spheres among them and/or with the walls of a container. Questions about the ergodic properties of these models (which can be mapped into billiard models) were first raised by Boltzmann in the nineteenth century and lie at the foundation of Statistical Mechanics. Billiard models also describe the diffusive motion of electrons bouncing off positive nuclei (Lorentz gas models) and in this situation the physical measure can be considered infinite. It is therefore of great importance to study the ergodic properties of maps when the measure they preserves is infinite. The aim of this thesis is to present an original result on smooth maps with singularities which preserve an infinite measure. Such result establishes the atomicity of the tail $\sigma$-algebra (and hence strong chaotic properties) in the presence of a totally conservative behavior.
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Vonseel, Audrey. "Hyperbolicité et bouts des graphes de Schreier." Thesis, Strasbourg, 2017. http://www.theses.fr/2017STRAD025/document.

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Cette thèse est consacrée à l'étude de la topologie à l'infini d'espaces généralisant les graphes de Schreier. Plus précisément, on considère le quotient X/H d'un espace métrique géodésique propre hyperbolique X par un groupe quasi-convexe-cocompact H d'isométries de X. On montre que ce quotient est un espace hyperbolique. Le résultat principal de cette thèse indique que le nombre de bouts de l'espace quotient X/H est déterminé par les classes d'équivalence sur une sphère de rayon explicitement calculable. Dans le cadre de la théorie des groupes, on montre que l'on peut construire explicitement des groupes et des sous-groupes pour lesquels il n'existe pas d'algorithme permettant de déterminer le nombre de bouts relatifs. Si le sous-groupe est quasi-convexe, on donne un algorithme permettant de calculer le nombre de bouts relatifs
This thesis is devoted to the study of the topology at infinity of spaces generalizing Schreier graphs. More precisely, we consider the quotient X/H of a geodesic proper hyperbolic metric space X by a quasiconvex-cocompact group H of isometries of X. We show that this quotient is a hyperbolic space. The main result of the thesis indicates that the number of ends of the quotient space X/H is determined by equivalence classes on a sphere of computable radius. In the context of group theory, we show that one can construct explicitly groups and subgroups for which there are no algorithm to determine the number of relative ends. If the subgroup is quasiconvex, we give an algorithm to compute the number of relative ends
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Jiang, Kai. "Normalisation C-infini des systèmes complètement intégrables." Thesis, Sorbonne Paris Cité, 2016. http://www.theses.fr/2016USPCC298/document.

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Cette thèse est consacrée à l’étude de la linéarisation géométrique locale des systèmes complètement intégrables dans la catégorie C1. Le sujet est la conjecture de linéarisation géométrique proposée (et établie dans le cadre analytique) par Nguyen Tien Zung. Nous commençons par les systèmes linéaires, puis introduisons la normalisation dans la catégorie formelle. Nous montrons qu’un système intégrable peut être décomposé en une partie hyperbolique et une partie elliptique. Nous établissons une bonne forme normale de Poincaré-Dulac pour les champs de vecteurs et discutons sa relation avec la linéarisation géométrique. Nous montrons que les systèmes intégrables faiblement hyperboliques sont géométriquement linéarisables en utilisant les outils de Chaperon. Nous étudions les systèmes intégrables sur les espaces de petite dimension : si celle-ci n’est pas plus grande que 4, alors la plupart des cas sont géométriquement linéarisables ; en particulier, la linéarisation géométrique est possible pour les systèmes intégrables de type de foyer-foyer. Enfin, nous généralisons la démonstration en grande dimension et proposons une condition sur les variétés fortement invariantes, sous laquelle nous linéarisons géométriquement les systèmes. Nous parvenons également à normaliser une action de R × T à plusieurs foyers en nous référant aux idées de Zung
This thesis is devoted to the local geometric linearization of completely integrable systems in the C1 category. The subject is the geometric linearization conjecture proposed (and proved in the analytic case) by Nguyen Tien Zung. We start from linear systems and introduce normalization in the formal category. Wes how that an integrable system can be decomposed into a hyperbolic part and an elliptic part. We establish a good Poincaré-Dulac normal form for the vector fields and discuss its relation with geometric linearization. We prove that weakly hyperbolic integrable systems are geometrically linearizable byusing Chaperon’s tools. We then study integrable systems on small dimensional spaces: if the dimension is no more than 4, then most cases are geometrically linearizable; in particular,geometric linearization works for integrable system of focus-focus type. Finally, we generalize the proof to high dimensions and propose a condition about strongly invariant manifolds, under which we linearize the systems in the geometric sense. We also manage to normalize an R × T-action of several focuses by referring to the ideas of Zung
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Saleur, Benoît. "Trois problèmes géométriques d'hyperbolicité complexe et presque complexe." Thesis, Paris 11, 2011. http://www.theses.fr/2011PA112256/document.

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Cette thèse est consacrée à l'étude de trois problèmes d'hyperbolicité complexe et presque complexe. La première partie est dédiée à la recherche d'une conséquence quantitative de l'hyperbolicité au sens de Kobayashi, qui est une propriété qualitative. Le résultat obtenu prend la forme d'une inégalité isopérimétrique qui évoque l'inégalité d'Ahlfors relative aux recouvrements des surfaces de surfaces. Sa démonstration est purement riemannienne.La deuxième partie de la thèse est consacrée à la démonstration d'une version presque complexe du théorème de Borel, qui affirme que les courbes entières dans le plan projectif complexe évitant quatre droites en position générale sont linéairement dégénérées. Dans un plan projectif presque complexe, les J-droites substituent aux droites projectives et nous disposons d'un énoncé analogue pour les J-courbes entières. La démonstration de ce résultat repose sur l'utilisation de projections centrales et sur la théorie de recouvrement des surfaces d'Ahlfors.La dernière partie est consacrée à la démonstration d'une version presque complexe du théorème de Bloch, qui affirme qu'une suite non normale de disques holomorphes du plan projectif évitant quatre droites en position générale converge, en un certain sens, vers une réunion de trois droites. Notre résultat implique en particulier l'hyperbolicité du complémentaire dans le plan projectif presque complexe de quatre J-droites modulo trois J-droites
This thesis is dedicated to the study of three problems of complex and almost complex hyperbolicity. Its first part is dedicated to the research of a quantitative consequence to Kobayashi hyperbolicity, which is a qualitative property. The result we obtain has the form of an isoperimetric inequality that suggests Ahlfors' inequality, the central result of the theory of covering surfaces. Its proof uses only riemannian tools.The second part of the thesis is dedicated to the proof of an almost complex version of Borel's theorem, which says that an entire curve in the compex preojective plane missing four lines in general position is degenerate. In an almost compex context, we can obtain a similar result for entire J-curves just by replacing projective lines by J-lines. The proof of this result uses central projections and Ahlfors' theory of covering surfaces.The last part is dedicated to the proof of an almost complex version of Bloch's theorem, which says that given a sequence of holomorphic discs in the projective plane, either it is normal, either it converges in some sens to a reunion of three lines. Our result will show in particular that the complementary set of four J-lines in general position is hyperbolic modulo three J-lines
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Petit, Camille. "Autour de l'analyse géométrique. 1) Comportement au bord des fonctions harmoniques 2) Rectifiabilité dans le groupe de Heisenberg." Phd thesis, Université de Grenoble, 2012. http://tel.archives-ouvertes.fr/tel-00744491.

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Dans cette thèse, nous nous intéressons à deux thèmes d'analyse géométrique. Le premier concerne le comportement asymptotique des fonctions harmoniques en relation avec la géométrie, sur des graphes et des variétés. Nous étudions des critères de convergence au bord des fonctions harmoniques, comme celui de la bornitude non-tangentielle, de la finitude de l'énergie ou encore de la densité de l'énergie. Nous nous plaçons pour cela dans différents cadres comme les graphes hyperboliques au sens de Gromov, les variétés hyperboliques au sens de Gromov, les graphes de Diestel-Leader ou encore dans un cadre abstrait pour obtenir des résultats pour les points du bord minimal de Martin. Les méthodes probabilistes utilisées exploitent le lien entre les fonctions harmoniques et les martingales. Le deuxième thème abordé dans cette thèse concerne l'étude des propriétés des ensembles rectifiables de dimension 1 dans le groupe de Heisenberg, en relation avec des opérateurs d'intégrales singulières. Nous étendons à ce contexte sous-riemannien une partie des résultats de la théorie des ensembles uniformément rectifiables de David et Semmes. Nous obtenons notamment un théorème géométrique du voyageur de commerce qui fournit une condition pour qu'un ensemble Ahlfors-régulier du premier groupe de Heisenberg soit contenu dans une courbe Ahlfors-régulière.
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Crawford, William. "Oka theory of Riemann surfaces." Thesis, 2014. http://hdl.handle.net/2440/84514.

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In his 1993 paper, J. Winkelmann determined the precise pairs of Riemann surfaces for which every continuous map between them can be deformed to a holomorphic map. In particular, it is true for all maps from non-compact Riemann surfaces into C, C*, the Riemann sphere or complex tori. This is a result of M. Gromov's seminal paper in 1989, where he introduced elliptic manifolds and showed that every continuous map from a Stein manifold into an elliptic manifold can be deformed to a holomorphic map. The elliptic Riemann surfaces are C, C*, the Riemann sphere and complex tori. Gromov incorporated versions of the Weierstrass and Runge approximation theorems into the deformation to get stronger Oka properties, known as BOPAI and BOPAJI in the literature. It has since been shown, using deep, higher dimensional techniques, that maps from Stein manifolds into elliptic manifolds satisfy BOPAI and BOPAJI. In this thesis we strengthen Winkelmann's results to find the precise pairs of Riemann surfaces that satisfy the stronger Oka properties of BOPAI and BOPAJI. We rely on Riemann surface theory, Morse theory and algebraic topology, rather than techniques from higher dimensional complex analysis.
Thesis (M.Phil.) -- University of Adelaide, School of Mathematical Sciences, 2014
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Books on the topic "Hyperbolicity theory"

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Júnior, Jacob Palis. Hyperbolicity and sensitive chaotic dynamicas at homoclinic bifurcaitons. Cambridge: Cambridge University Press, 1993.

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Floris, Takens, ed. Hyperbolicity and sensitive chaotic dynamics at homoclinic bifurcations: Fractal dimensions and infinitely many attractors. Cambridge: Cambridge University Press, 1993.

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Valls, Claudia, Luís Barreira, and Davor Dragičević. Admissibility and Hyperbolicity. Springer, 2018.

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Takens, Floris, and Jacob Palis. Hyperbolicity and Sensitive Chaotic Dynamics at Homoclinic Bifurcations: Fractal Dimensions and Infinitely Many Attractors in Dynamics (Cambridge Studies in Advanced Mathematics). Cambridge University Press, 1993.

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Verbaarschot, Jac. Quantum chaos and quantum graphs. Edited by Gernot Akemann, Jinho Baik, and Philippe Di Francesco. Oxford University Press, 2018. http://dx.doi.org/10.1093/oxfordhb/9780198744191.013.33.

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This article examines the origins of the universality of the spectral statistics of quantum chaotic systems in the context of periodic orbit theory. It also considers interesting analogies between periodic orbit theory and the sigma model, along with related work on quantum graphs. The article first reviews some facts and definitions for classically chaotic systems in order to elucidate their quantum behaviour, focusing on systems with two degrees of freedom: one characterized by ergodicity and another by hyperbolicity. It then describes two semiclassical approximation techniques — Gutzwiller’s periodic orbit theory and a refined approach incorporating the unitarity of the quantum evolution — and highlights their importance in understanding universal spectral statistics, and how they are related to the sigma model. This is followed by an analysis of parallel developments for quantum graphs, which are relevant to quantum chaos.
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Zeitlin, Vladimir. Rotating Shallow-Water Models as Quasilinear Hyperbolic Systems, and Related Numerical Methods. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198804338.003.0007.

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The chapter contains the mathematical background necessary to understand the properties of RSW models and numerical methods for their simulations. Mathematics of RSW model is presented by using their one-dimensional reductions, which are necessarily’one-and-a-half’ dimensional, due to rotation and include velocity in the second direction. Basic notions of quasi-linear hyperbolic systems are recalled. The notions of weak solutions, wave breaking, and shock formation are introduced and explained on the example of simple-wave equation. Lagrangian description of RSW is used to demonstrate that rotation does not prevent wave-breaking. Hydraulic theory and Rankine–Hugoniot jump conditions are formulated for RSW models. In the two-layer case it is shown that the system loses hyperbolicity in the presence of shear instability. Ideas of construction of well-balanced (i.e. maintaining equilibria) shock-resolving finite-volume numerical methods are explained and these methods are briefly presented, with illustrations on nonlinear evolution of equatorial waves.
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Book chapters on the topic "Hyperbolicity theory"

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Diverio, Simone, and Erwan Rousseau. "Kobayashi hyperbolicity: basic theory." In Hyperbolicity of Projective Hypersurfaces, 1–9. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-32315-2_1.

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Ancona, Alano. "Positive harmonic functions and hyperbolicity." In Potential Theory Surveys and Problems, 1–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0103341.

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Dumortier, Freddy, and Robert Roussarie. "Geometric Singular Perturbation Theory Beyond Normal Hyperbolicity." In Multiple-Time-Scale Dynamical Systems, 29–63. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4613-0117-2_2.

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Yamanoi, Katsutoshi. "Kobayashi Hyperbolicity and Higher-dimensional Nevanlinna Theory." In Geometry and Analysis on Manifolds, 209–73. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-11523-8_9.

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Church, Kevin E. M., and Xinzhi Liu. "Hyperbolicity and the Classical Hierarchy of Invariant Manifolds." In Bifurcation Theory of Impulsive Dynamical Systems, 139–49. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-64533-5_7.

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Cai, Zhenning, Yuwei Fan, and Ruo Li. "Hyperbolic Model Reduction for Kinetic Equations." In SEMA SIMAI Springer Series, 137–57. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-030-86236-7_8.

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AbstractWe make a brief historical review of the moment model reduction for the kinetic equations, particularly Grad’s moment method for Boltzmann equation. We focus on the hyperbolicity of the reduced model, which is essential for the existence of its classical solution as a Cauchy problem. The theory of the framework we developed in the past years is then introduced, which preserves the hyperbolic nature of the kinetic equations with high universality. Some lastest progress on the comparison between models with/without hyperbolicity is presented to validate the hyperbolic moment models for rarefied gases.
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Lokshin, Alexander A. "The Problem of Hyperbolicity in Linear Hereditary Elasticity." In Tauberian Theory of Wave Fronts in Linear Hereditary Elasticity, 1–29. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-8578-4_1.

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Voiculescu, Dan. "Perturbations of Operators, Connections with Singular Integrals, Hyperbolicity and Entropy." In Harmonic Analysis and Discrete Potential Theory, 181–91. Boston, MA: Springer US, 1992. http://dx.doi.org/10.1007/978-1-4899-2323-3_14.

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Rossikhin, Yury A., and Marina V. Shitikova. "Dynamic Equations, Verification of Hyperbolicity via the Theory of Discontinuities." In Encyclopedia of Continuum Mechanics, 1–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 2018. http://dx.doi.org/10.1007/978-3-662-53605-6_106-1.

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Rossikhin, Yury A., and Marina V. Shitikova. "Dynamic Equations, Verification of Hyperbolicity via the Theory of Discontinuities." In Encyclopedia of Continuum Mechanics, 691–702. Berlin, Heidelberg: Springer Berlin Heidelberg, 2020. http://dx.doi.org/10.1007/978-3-662-55771-6_106.

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Conference papers on the topic "Hyperbolicity theory"

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Sondermann, Carina N., Rodrigo A. C. Patrício, Aline B. Figueiredo, Renan M. Baptista, Felipe B. F. Rachid, and Gustavo C. R. Bodstein. "Hyperbolicity Analysis of a One-Dimensional Two-Fluid Two-Phase Flow Model for Stratified-Flow Pattern." In ASME 2015 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/imece2015-51587.

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Two-phase flows in pipelines occur in a variety of processes in the nuclear, petroleum and gas industries. Because of the practical importance of accurately predicting steady and unsteady flows along the line, one-dimensional two-fluid flow models have been extensively employed in numerical simulations. These models are usually written as a system of non-linear hyperbolic partial-differential equations, but some of the available formulations are physically inconsistent due to a loss of the hyperbolicity property. In these cases, the associated eigenvalues become complex numbers and the model loses physical meaning locally. This paper presents a numerical study of a one-dimensional single-pressure four-equation two-fluid model for an isothermal stratified flow that occurs in a horizontal pipeline. The diameter, pressure and volume fraction are kept constant, whereas the liquid and gas velocities are varied to cover the entire range of superficial velocities in the stratified region. For each point, the eigenvalues are numerically computed to verify whether they are real numbers and to assess their signs. The results show that hyperbolicity is lost near the boundaries of the stratified pattern and in a vast area of the region itself. Moreover, the eigenvalue signs alternate, which has implications on the prescription of numerical boundary conditions.
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Sondermann, Carina N., Raphael V. N. de Freitas, Rodrigo A. C. Patricio, Aline B. Figueiredo, Gustavo C. R. Bodstein, Felipe B. F. Rachid, and Renan M. Baptista. "A Hyperbolicity Analysis of the 1991 OLGA’s Model for Isothermal Flow." In ASME 2018 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2018. http://dx.doi.org/10.1115/imece2018-87513.

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Multiphase flows are encountered in many engineering problems. Particularly in the oil and gas industry, many applications involve the transportation of a mixture of oil and natural gas in long pipelines from offshore platforms to the continent. Numerical simulations of steady and unsteady flows in pipelines are usually based on one-dimensional models, such as the two-fluid model, the drift-flux model and the homogeneous equilibrium model. The 1991’s version of the well-known and widely-used commercial software OLGA describes a system of non-linear equations of the two-fluid-model type, with an extra equation for the presence of liquid droplets. It is well known that one-dimensional formulations may be physically inconsistent due to the loss of hyperbolicity. In these cases, the associated eigenvalues become complex numbers and the model loses physical meaning locally. This paper presents a numerical study of the 1991’s version of the software OLGA, for an isothermal flow of stratified pattern, in a horizontal pipeline. For each point of interest in the stratified-pattern flow map, the eigenvalues are numerically calculated in order to verify if the eigenvalues are real and also to assess their signs. The results indicate that the model is conditionally hyperbolic and loses hyperbolicity in a vast area of the stratified region under certain flow conditions. Even though the model is not unconditionally hyperbolic, some simulations here performed for typical offshore pipeline flows are shown to be in the hyperbolic region.
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Eini, Tomer, Tal Asherov, Yarden Mazor, and Itai Epstein. "Valley-polarized Hyperbolic-Exciton-Polaritons in 2D Semiconductors." In CLEO: QELS_Fundamental Science. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/cleo_qels.2022.fm1a.4.

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In this work, we predict the existence of hyperbolic-exciton-polaritons (HEPs) in 2D semiconductors of transition-metal-dichalcogenides (TMDs) at visible frequencies. We show that hyperbolicity can be induced in the layered material owing to the behavior of the excitons supported by the TMD, therefore leading to the existence of HEPs. We derive the HEPs dispersion relation, analyzing their confinement and loss properties and finding the HEPs’ wavelengths are about two orders of magnitude smaller than the corresponding free-space wavelength. Furthermore, we show that the existing HEPs are coupled to the valley degree-of-freedom, leading to a hyperbolic spin-valley hall effect.
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Nourgaliev, Robert, Nam Dinh, and Theo Theofanous. "A Characteristics-Based Approach to the Numerical Solution of the Two-Fluid Model." In ASME/JSME 2003 4th Joint Fluids Summer Engineering Conference. ASMEDC, 2003. http://dx.doi.org/10.1115/fedsm2003-45551.

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This paper is concerned with numerical solutions of the two-fluid models of two-phase flow. The two-fluid modeling approach is based on the effective-field description of inter-penetrating continua and uses constitutive laws to account for the inter-field interactions. The effective-field balance equations are derived by a homogenization procedure and known to be non-hyperbolic. Despite their importance and widespread application, predictions by such models have been hampered by numerical pitfalls manifested in the formidable challenge to obtain convergent numerical solutions under computational grid refinement. At the root of the problem is the absence of hyperbolicity in the field equations and the resulting ill-posedness. The aim of the present work is to develop a high-order-accurate numerical scheme that is not subject to such limitations. The main idea is to separate conservative and non-conservative parts, by implementing the latter as part of the source term. The conservative part, being effectively hyperbolic, is treated by a characteristics-based method. The scheme performance is examined on a compressible-incompressible two-fluid model. Convergence of numerical solutions to the analytical one is demonstrated on a benchmark (water faucet) problem.
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