| 摘要 | 第8-9页 |
| Abstract | 第9页 |
| Prefaces | 第10-18页 |
| Chapter 1 Multifractal Analysis of Ergodic Averages in Some Nonuni-formly Hyperbolic Systems | 第18-34页 |
| 1.1 Preliminaries and Main Result | 第18-21页 |
| 1.2 Proof of Main Results | 第21-32页 |
| 1.2.1 Upper Bound on P(X(φ,U),ψ) | 第21页 |
| 1.2.2 Lower Bound on P(X(φ,U),ψ) | 第21-32页 |
| 1.3 Some Applications | 第32-34页 |
| Chapter 2 The Historic Set for Continuous Maps with Non-uniform Spec-ification Property | 第34-46页 |
| 2.1 Proof of Main Result | 第34-44页 |
| 2.1.1 Construction of the fractal F | 第36-38页 |
| 2.1.2 Construction of a special sequence of measures μk | 第38-39页 |
| 2.1.3 Proof of Theorem 2.1.1 | 第39-42页 |
| 2.1.4 Modification to Obtain Theorem 2.0.1 | 第42-44页 |
| 2.2 Some Examples | 第44-46页 |
| Chapter 3 Pesin Theory and Weak Shadowing Property | 第46-49页 |
| Chapter 4 The Conditional Variational Principle for Dynamical Systems with Weak Shadowing Property | 第49-67页 |
| 4.1 Proof of Theorem 4.0.1 | 第50-65页 |
| 4.1.1 Katok's Definition of Metric Entropy | 第51-52页 |
| 4.1.2 Some Lemmas | 第52-54页 |
| 4.1.3 Proof of Theorem 4.1.1 | 第54-65页 |
| 4.2 Proof of Theorem 4.0.2 | 第65-66页 |
| 4.3 Applications | 第66-67页 |
| Chapter 5 Conditional Variational Principle for Historic Set for Systems with Weak Shadowing Property | 第67-78页 |
| 5.1 Main Results | 第67-69页 |
| 5.2 Proof of Theorem 5.1.1 | 第69-75页 |
| 5.3 Applications | 第75-78页 |
| Chapter 6 Large Deviation Properties in Some Nonuniformly Hyperbolic Systems | 第78-87页 |
| 6.1 Preliminaries and Main Result | 第78-79页 |
| 6.2 Proof of Main Theorem | 第79-86页 |
| 6.3 Application | 第86-87页 |
| Bibliography | 第87-91页 |
| Acknowledgements | 第91-92页 |
| Publications or Accepted Papers | 第92-93页 |
| Further researches | 第93页 |
