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Relevant bibliographies by topics / Hyperbolic dynamical systems

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Dissertations / Theses

Academic literature on the topic 'Hyperbolic dynamical systems'

Author: Grafiati

Published: 7 December 2024

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Dissertations / Theses on the topic "Hyperbolic dynamical systems"

1

Ponce, Gabriel. "Fine ergodic properties of partially hyperbolic dynamical systems." Universidade de São Paulo, 2014. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-20032015-113539/.

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Let f : T3 → T3 be a C2 volume preserving partially hyperbolic diffeomorphism homotopic to a linear Anosov automorphism A : T3 → T3. We prove that if f is Kolmogorov, then f is Bernoulli. We study the characteristics of atomic disintegration of the volume measure whenever it occurs. We prove that if the volume measure m has atomic disintegration on the center leaves then the disintegration has one atom per center leaf. We give a condition, depending only on the center Lyapunov exponent of the diffeomorphism, that guarantees atomic disintegration of the volume measure on center leav

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2

Petty, Taylor Michael. "Nonlocally Maximal Hyperbolic Sets for Flows." BYU ScholarsArchive, 2015. https://scholarsarchive.byu.edu/etd/5558.

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In 2004, Fisher constructed a map on a 2-disc that admitted a hyperbolic set not contained in any locally maximal hyperbolic set. Furthermore, it was shown that this was an open property, and that it was embeddable into any smooth manifold of dimension greater than one. In the present work we show that analogous results hold for flows. Specifically, on any smooth manifold with dimension greater than or equal to three there exists an open set of flows such that each flow in the open set contains a hyperbolic set that is not contained in a locally maximal one.

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3

Al-Nayef, Anwar Ali Bayer, and mikewood@deakin edu au. "Semi-hyperbolic mappings in Banach spaces." Deakin University. School of Computing and Mathematics, 1997. http://tux.lib.deakin.edu.au./adt-VDU/public/adt-VDU20051208.110247.

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The definition of semi-hyperbolic dynamical systems generated by Lipschitz continuous and not necessarily invertible mappings in Banach spaces is presented in this thesis. Like hyperbolic mappings, they involve a splitting into stable and unstable spaces, but a slight leakage from the strict invariance of the spaces is possible and the unstable subspaces are assumed to be finite dimensional. Bi-shadowing is a combination of the concepts of shadowing and inverse shadowing and is usually used to compare pseudo-trajectories calculated by a computer with the true trajectories. In this thesis, the

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4

Gaito, Stephen Thomas. "Shadowing of weakly pseudo-hyperbolic pseudo-orbits in discrete dynamical systems." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/109461/.

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We consider Cr (r ≥ 1 +γ) diffeomorphisms of compact Riemannian manifolds. Our aim is to develop the analytic machinery required to describe the topological symbolic dynamics of sets of weakly hyperbolic orbits. The Pesin set is an example of such a set. For Axiom-A dynamical systems, that is, for diffeomorphisms which have a uniformly hyperbolic nonwandering set which is the closure of the periodic orbits, this analytic machinery is provided by the Shadowing Lemma. This lemma is a consequence of the Stable Manifold Theorem, and the local product structure of the nonwandering set of an Axiom-A

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5

Waddington, Simon. "Prime orbit theorems for closed orbits and knots in hyperbolic dynamical systems." Thesis, University of Warwick, 1992. http://wrap.warwick.ac.uk/109425/.

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This thesis consists of four chapters, each with its own notation and references. Chapters 1, 2 and 3 are independent pieces of research. Chapter 0 is an introduction which sets out the definitions and results needed in the main part of the thesis. In Chapter 1, we derive asymptotic formulae for the number of closed orbits of a toral automorphism which is ergodic, but not necessarily hyperbolic. Previously, such formulae were known only in the hyperbolic case. The proof uses an analogy with the Prime Number Theorem. We also give a new proof of the uniform distribution of periodic points. In Ch

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6

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 e

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7

Leclerc, Gaétan. "Nonlinearity, fractals, Fourier decay - harmonic analysis of equilibrium states for hyperbolic dynamical systems." Electronic Thesis or Diss., Sorbonne université, 2024. http://www.theses.fr/2024SORUS264.

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Ce doctorat se situe à l'intersection entre le domaine de la géométrie fractale et des systèmes dynamique hyperbolique. Étant donné un système dynamique hyperbolique dans un espace euclidien (de petite dimension), considérons un sous-ensemble fractal compact invariant, ainsi qu'une mesure de probabilité invariante supportée sur cet ensemble fractal, avec de bonnes propriétés statistiques, telle que la mesure d'entropie maximale. La question est la suivante : la transformée de Fourier de la mesure tends elle vers zéro a la vitesse d'une puissance de xi ? Notre objectif principal est de montrer

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8

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.<br/>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...). <br/>Genèricament, qualse

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9

Högele, Michael, and Ilya Pavlyukevich. "Metastability of Morse-Smale dynamical systems perturbed by heavy-tailed Lévy type noise." Universität Potsdam, 2014. http://opus.kobv.de/ubp/volltexte/2014/7063/.

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We consider a general class of finite dimensional deterministic dynamical systems with finitely many local attractors each of which supports a unique ergodic probability measure, which includes in particular the class of Morse–Smale systems in any finite dimension. The dynamical system is perturbed by a multiplicative non-Gaussian heavytailed Lévy type noise of small intensity ε > 0. Specifically we consider perturbations leading to a Itô, Stratonovich and canonical (Marcus) stochastic differential equation. The respective asymptotic first exit time and location problem from each of the domai

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10

Canadell, Cano Marta. "Computation of Normally Hyperbolic Invariant Manifolds." Doctoral thesis, Universitat de Barcelona, 2014. http://hdl.handle.net/10803/277215.

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The subject of the theory of Dynamical Systems is the evolution of systems with respect to time. Hence, it has many applications to other areas of science, such as Physics, Biology, Economics, etc. and it also has interactions with other parts of Mathematics. The global behavior of a dynamical system is organized by its invariant objects, the simplest ones are equilibria and periodic orbits (and related invariant manifolds). Normally hyperbolic invariant manifolds (NHIM for short) are some of these invariant objects. They have the property to persist under small perturbations of the system.

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