| 中文摘要 | 第1-6页 |
| Abstract | 第6-10页 |
| 前言 | 第10-15页 |
| Chapter 1 Stability and the growth of the number of closed characteristics on compact convex hypersurfaces | 第15-26页 |
| ·Introduction and main results | 第15-17页 |
| ·Proof of Theorem 1 | 第17-21页 |
| ·Proof of Theorem 2 | 第21-26页 |
| Chapter 2 Symmetric closed characteristics on symmetric compact convex hypersurfaces | 第26-71页 |
| ·Introduction and main results | 第26-29页 |
| ·Stability of symmetric closed characteristics on symmetric compact convex hy- persurfaces in R2nunder a pinching condition | 第29-42页 |
| ·Critical point theory for symmetric closed characteristics | 第29-31页 |
| ·Index iteration theory for symmetric closed characteristics | 第31-37页 |
| ·Proofs of the main theorems | 第37-42页 |
| ·Resonance identity for symmetric closed characteristics on symmetric convex Hamiltonian energy surfaces with its applications | 第42-71页 |
| ·A variational structure for symmetric closed characteristics | 第42-45页 |
| ·Critical modules for symmetric closed characteristics | 第45-59页 |
| ·Homological vanishing near the origin | 第59-61页 |
| ·Proof of the Theorem 5 | 第61-64页 |
| ·Multiplicity and stability of symmetric closed characteristics | 第64-69页 |
| ·Generic existence of infinitely many symmetric closed characteristics | 第69-71页 |
| Chapter 3 Resonance identity and multiplicity of closed characteristics on compact star-shaped hypersurfaces | 第71-120页 |
| ·Introduction and main results | 第71-75页 |
| ·Variational structure for closed characteristics and finite dimensional reduction | 第75-83页 |
| ·Parameter independence of critical modules for closed characteristics | 第83-95页 |
| ·Periodic property of critical modules for closed characteristics | 第95-104页 |
| ·Contribution of the origin | 第104-106页 |
| ·Proof of Theorem 10 | 第106-110页 |
| ·Multiplicity of closed characteristics on star-shaped hypersurfaces | 第110-115页 |
| ·Appendix: A brief review on an index theory for symplectic paths | 第115-120页 |
| Chapter 4 Multiple P-invariant closed characteristics on partially symmetric compact convex hypersurfaces in R2n | 第120-146页 |
| ·Introduction and main results | 第120-122页 |
| ·Critical point theory for P-invariant closed characteristics | 第122-132页 |
| ·A variational structure for P-invariant closed characteristics | 第122-127页 |
| ·Equivariant Morse theory for P-invariant closed characteristics | 第127-132页 |
| ·Index theory for P-invariant closed characteristics and a brief review on (P, ω)-index theory | 第132-141页 |
| ·Maximal index jump and the proof of the main theorem | 第141-146页 |
| 参考文献 | 第146-150页 |
| 致谢 | 第150-151页 |
| 个人简历与已完成的论文 | 第151-152页 |
