Surface laminations and chaotic dynamical systems

Surface laminations and chaotic dynamical systems
Vyacheslav Grines, Evgeny Zhuzhoma Серия Динамические системы и робототехника ISBN 978-5-4344-0858-5 Издательство «ИКИ» 2021 г.
Переплет, 502 стр.
Формат 60*84 1/16
Вес  905 г


CHAPTER 1. Foundations1.1. Manifolds1.2. Definition of a Dynamical System1.3. Elements of Topological Dynamics1.4. Linear maps1.5. Grobman-Hartman Theorem1.6. Hyperbolic Sets1.7. Basic Theorems for Hyperbolic Sets1.8. Nontrivial attractors and repellers1.9. Expansiveness,mixing, and shadowingBibliographicNotes and Panoramas
CHAPTER 2. Dynamics of Degree One Circle Maps2.1. Degree of circle maps2.2. The Poincar´e rotation number2.3. Circle maps with irrational rotation numberBibliographicNotes and Panoramas
CHAPTER 3. Introduction to Local Laminations3.1. First notations and examples3.2. Basic specification methods3.3. Limit sets of a curve and leaf3.4. Orientable and non-orientable local laminations3.5. Closed transversals3.6. Index of closed curve and singularity3.7. Minimal and quasiminimal sets3.8. Geodesic laminationsBibliographicNotes and Panoramas
CHAPTER 4. Poincar´e -Bendixson Theory for Local Laminations4.1. Poincar´e-Bendixson Theorems for Local Laminations4.2. Bendixson theorems4.3. Cherry theorem4.4. Maier theoremsBibliographicNotes and Panoramas
CHAPTER 5. Introduction to Anosov -Weil Theory5.1. Introductory concepts and notions5.2. The theoremand conjecture ofWeil5.3. Anosov theorems on asymptotic directions and approximations of curves5.4. Nonlocal asymptotic behavior of special curves5.5. Geodesic frameworks of local laminations5.6. Deviations of curves fromco-asymptotic geodesics5.7. How smoothness depends on asymptotic directions5.8. The image of geodesic under a cover homeomorphismBibliographicNotes and Panoramas
CHAPTER 6. Classification of Surface Foliations, Webs, and Homeomorphisms6.1. Elements of the Nielsen-Thurston Theory6.2. Irrational foliations on 2-torus6.3. Irrational foliations on hyperbolic surfaces6.4. Classification of irrational 2-webs6.5. Classification of Denjoy flows and nontrivial minimal sets6.6. Surface AP-homeomorphisms6.7. Nielsen Theory revisitedBibliographicNotes and Panoramas
CHAPTER 7. Chaotic Dynamical Systems with Minimal Entropy7.1. Properties of hyperbolic automorphisms7.2. Geodesic laminations and hyperbolic automorphisms7.3. Strongly irrational transversal geodesic lamination7.4. Hyperbolic homeomorphisms induced by hyperbolic automorphisms7.5. Topological entropy of hyperbolic homeomorphismsBibliographicNotes and Panoramas
CHAPTER 8. One-Dimensional Attractors and Aranson -Grines homeomorphisms8.1. Asymptotic behaviors of stable and unstablemanifolds8.2. Geodesic frameworks of widely disposed attractors8.3. Classification TheoremBibliographicNotes and Panoramas
CHAPTER 9. Structural Stability and Anosov -Weil Theory9.1. Asymptotic properties of invariantmanifolds9.2. Conditions of bound deviation of invariant manifolds from coasymptotic geodesicsBibliographicNotes and PanoramasBibliography