| Chapter 1 The High Dimensional Melnikov Method with Nonresonance | 第1-33页 |
| ·Introduction | 第19-22页 |
| ·The geometric structure of the unperturbed System 1 | 第22-26页 |
| ·The geometric structure of the perturbed phase space | 第26-33页 |
| Chapter 2 On the Persistence of Lower Dimensional Invariant Tori for Hamiltonian Systems | 第33-53页 |
| ·Introduction | 第33-36页 |
| ·Some elementary reviews | 第36-40页 |
| ·Main results and proof | 第40-50页 |
| ·Time-dependent quasi-periodic perturbation | 第50-53页 |
| Chapter 3 Some Dynamics in the ABC Flow | 第53-64页 |
| ·Introduction | 第53-54页 |
| ·Structure of the ABC flow with C=0 | 第54-56页 |
| ·Invariant tori in the ABC flow with C≠0 | 第56-61页 |
| ·Chaotic streamlines in the ABC flow with C≠0 | 第61-64页 |
| Chapter 4 Geometric Singular Perturbation Theory with Resonance | 第64-75页 |
| ·Introduction | 第64-65页 |
| ·The set up | 第65-69页 |
| ·Main results | 第69-75页 |
| Chapter 5 Spectral Approximation of Attractors tbr the Damped and Driven Periodically Sine-Gordon Equation | 第75-99页 |
| ·Introduction | 第75-77页 |
| ·General approximation results | 第77-81页 |
| ·The existence of a global attractor | 第81-91页 |
| ·Attractors under the spectral approximation and their convergence | 第91-99页 |
| Chapter 6 Mechanism Causing Chaotic Jumping Behavior in the Damped Driven Sine-Gordon Equation | 第99-120页 |
| ·Introduction | 第99-101页 |
| ·The ODE on GAIM of the sine-Gordon equation | 第101-105页 |
| ·Unperturbed structure | 第105-109页 |
| ·Perturbed structure and dynamics near the resonance | 第109-111页 |
| ·Homoclinic orbits and pulse orbits | 第111-120页 |
| Chapter 7 Exact Solutions of the Nonlinear Evolution Equations | 第120-140页 |
| ·Introduction | 第120-122页 |
| ·Frame of the method | 第122-125页 |
| ·Two examples | 第125-131页 |
| ·A family of interesting exact solutions of the sine-Gordon equation | 第131-140页 |
| References | 第140-144页 |
| Acknowledgement | 第144-145页 |
