应用非线性动力系统中的几个问题 英文版PDF电子书下载

Chapter 1 The High Dimensional Melnikov Method with Nonresonance 1

1.1 Introduction 1

1.2 The geometric structure of the unperturbed System I 4

1.3 The geometric structure of the perturbed phase space 8

Chapter 2 On the Persistence of Lower Dimensional Invariant Tori for Hamiltonian Systems 15

2.1 Introduction 15

2.2 Some elementary reviews 18

2.3 Main results and proof 22

2.4 Time-dependent quasi-periodic perturbation 32

Chapter 3 Some Dynamics in ABC Flow 35

3.1 Introduction 35

3.2 Structure of the ABC flow with C=0 36

3.3 Invariant tori in the ABC flow with C≠0 38

3.4 Chaotic streamlines in the ABC flow with C≠0 43

Chapter 4 Geometric Singular Perturbation Theory with Resonance 46

4.1 Introduction 46

4.2 The set up 47

4.3 Main results 51

Chapter 5 Spectral Approximation of Attractors for the Damped and Driven Periodically Sine-Gordon Equation 57

5.1 Introduction 57

5.2 General approximation results 59

5.3 The existence of a global attractor 63

5.4 Attractors under the spectral approximation and their convergence 73

Chapter 6 Mechanism Causing Chaotic Jumping Behavior in the Damped Driven Sine-Gordon Equation 81

6.1 Introduction 81

6.2 The ODE on GAIM of the sine-Gordon equation 83

6.3 Unperturbed structure 87

6.4 Perturbed structure and dynamics near the resonance 91

6.5 Homocline orbits and pulse orbits 93

Chapter 7 Exact Solutions of the Nonlinear Evolution Equations 102

7.1 Introduction 102

7.2 Frame of the method 104

7.3 Two examples 107

7.4 A family of interesting exact solutions of the sine-Gordon equation 113

References 122

Acknowledgement 126