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. Foundations
1.1. Manifolds
1.2. Definition of a Dynamical System
1.3. Elements of Topological Dynamics
1.4. Linear maps
1.5. Grobman-Hartman Theorem
1.6. Hyperbolic Sets
1.7. Basic Theorems for Hyperbolic Sets
1.8. Nontrivial attractors and repellers
1.9. Expansiveness,mixing, and shadowing
BibliographicNotes and Panoramas

CHAPTER 2. Dynamics of Degree One Circle Maps
2.1. Degree of circle maps
2.2. The Poincar´e rotation number
2.3. Circle maps with irrational rotation number
BibliographicNotes and Panoramas

CHAPTER 3. Introduction to Local Laminations
3.1. First notations and examples
3.2. Basic specification methods
3.3. Limit sets of a curve and leaf
3.4. Orientable and non-orientable local laminations
3.5. Closed transversals
3.6. Index of closed curve and singularity
3.7. Minimal and quasiminimal sets
3.8. Geodesic laminations
BibliographicNotes and Panoramas

CHAPTER 4. Poincar´e -Bendixson Theory for Local Laminations
4.1. Poincar´e-Bendixson Theorems for Local Laminations
4.2. Bendixson theorems
4.3. Cherry theorem
4.4. Maier theorems
BibliographicNotes and Panoramas

CHAPTER 5. Introduction to Anosov -Weil Theory
5.1. Introductory concepts and notions
5.2. The theoremand conjecture ofWeil
5.3. Anosov theorems on asymptotic directions and approximations of curves
5.4. Nonlocal asymptotic behavior of special curves
5.5. Geodesic frameworks of local laminations
5.6. Deviations of curves fromco-asymptotic geodesics
5.7. How smoothness depends on asymptotic directions
5.8. The image of geodesic under a cover homeomorphism
BibliographicNotes and Panoramas

CHAPTER 6. Classification of Surface Foliations, Webs, and Homeomorphisms
6.1. Elements of the Nielsen-Thurston Theory
6.2. Irrational foliations on 2-torus
6.3. Irrational foliations on hyperbolic surfaces
6.4. Classification of irrational 2-webs
6.5. Classification of Denjoy flows and nontrivial minimal sets
6.6. Surface AP-homeomorphisms
6.7. Nielsen Theory revisited
BibliographicNotes and Panoramas

CHAPTER 7. Chaotic Dynamical Systems with Minimal Entropy
7.1. Properties of hyperbolic automorphisms
7.2. Geodesic laminations and hyperbolic automorphisms
7.3. Strongly irrational transversal geodesic lamination
7.4. Hyperbolic homeomorphisms induced by hyperbolic automorphisms
7.5. Topological entropy of hyperbolic homeomorphisms
BibliographicNotes and Panoramas

CHAPTER 8. One-Dimensional Attractors and Aranson -Grines homeomorphisms
8.1. Asymptotic behaviors of stable and unstablemanifolds
8.2. Geodesic frameworks of widely disposed attractors
8.3. Classification Theorem
BibliographicNotes and Panoramas

CHAPTER 9. Structural Stability and Anosov -Weil Theory
9.1. Asymptotic properties of invariantmanifolds
9.2. Conditions of bound deviation of invariant manifolds from coasymptotic geodesics
BibliographicNotes and Panoramas