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Handbook of Dynamical Systems 动力系统手册
by Boris Hasselblatt, Anatole Katok
格式：pdf 页数：203 语言：英语
Contents
Chapter 1. Introduction 13
1. Purpose and structure 13
2. The basic objects of dynamics 14
3. Equivalence and functorial constructions 17
4. Asymptotic behavior and averaging 23
Chapter 2. Topological dynamics 27
1. Setting and examples 27
2. Basic concepts and constructions 29
3. Recurrence 33
4. Relative behavior of orbits 38
5. Orbit growth properties 40
6. Symbolic dynamical systems 48
7. Low-dimensional topological dynamical systems 54
Chapter 3. Ergodic theory 57
1. Introduction 57
2. Measure spaces, maps, and Lebesgue spaces 60
3. Setting and examples 63
4. Basic concepts and constructions 66
5. Ergodic theorems 71
6. Quantitative recurrence and principal spectral properties 74
7. Entropy 79
Chapter 4. Invariant measures intopological dynamics 89
1. Introduction 89
2. Existence of invariant measures 89
3. Unique ergodicity 93
4. Metric and topological entropy 97
Chapter 5. Smooth, Hamiltonian and Lagrangian dynamics 103
1. Differentiable dynamics 103
2. Basic concepts and constructions 109
3. Hamiltonian dynamics 119
4. Lagrangian systems 123
5. Contact systems 125
6. Variational methodsin dynamics 127
7. Holomorphic dynamics 130
Chapter 6. Hyperbolic dynamics: Orbit instability and structural stability 133
1. Introduction 133
2. Main features of hyperbolic behavior 134
3. Stable manifolds 136
4. Definitions 137
5. Examples 139
6. The core theory 141
7. Developments of the theory 145
8. The theory of nonuniformly hyperbolic systems 150
9. Partial hyperbolicity 152
Chapter 7. Elliptic dynamics: Stable recurrent behavior 155
1. Introduction 155
2. The setting for elliptic dynamics 158
3. Diophantine phenomena with a single frequency 164
4. Diophantine phenomena with several frequencies 170
5. Liouvillian phenomena 172
Chapter 8. Parabolic dynamics: A special case of intermediate orbit growth 177
1. Introduction 177
2. Main features of parabolic behavior 178
3. Parabolic systems with uniform structure 181
4. Flows on surfaces 183
5. Billiards in polygons and polyhedra and related systems 188
Bibliography 195
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