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应用非线性动力系统中的几个问题 英文版PDF|Epub|txt|kindle电子书版本网盘下载
- 黄德斌著 著
- 出版社： 上海：上海大学出版社
- ISBN：7810581465
- 出版时间：2000
- 标注页数：126页
- 文件大小：3MB
- 文件页数：147页
- 主题词：
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图书目录
Chapter 1 The High Dimensional Melnikov Method with Nonresonance1
1.1 Introduction1
1.2 The geometric structure of the unperturbed System I4
1.3 The geometric structure of the perturbed phase space8
Chapter 2 On the Persistence of Lower Dimensional Invariant Tori for Hamiltonian Systems15
2.1 Introduction15
2.2 Some elementary reviews18
2.3 Main results and proof22
2.4 Time-dependent quasi-periodic perturbation32
Chapter 3 Some Dynamics in ABC Flow35
3.1 Introduction35
3.2 Structure of the ABC flow with C=036
3.3 Invariant tori in the ABC flow with C≠038
3.4 Chaotic streamlines in the ABC flow with C≠043
Chapter 4 Geometric Singular Perturbation Theory with Resonance46
4.1 Introduction46
4.2 The set up47
4.3 Main results51
Chapter 5 Spectral Approximation of Attractors for the Damped and Driven Periodically Sine-Gordon Equation57
5.1 Introduction57
5.2 General approximation results59
5.3 The existence of a global attractor63
5.4 Attractors under the spectral approximation and their convergence73
Chapter 6 Mechanism Causing Chaotic Jumping Behavior in the Damped Driven Sine-Gordon Equation81
6.1 Introduction81
6.2 The ODE on GAIM of the sine-Gordon equation83
6.3 Unperturbed structure87
6.4 Perturbed structure and dynamics near the resonance91
6.5 Homocline orbits and pulse orbits93
Chapter 7 Exact Solutions of the Nonlinear Evolution Equations102
7.1 Introduction102
7.2 Frame of the method104
7.3 Two examples107
7.4 A family of interesting exact solutions of the sine-Gordon equation113
References122
Acknowledgement126