| 摘要 | 第8-9页 |
| Abstract | 第9页 |
| Prefaces | 第10-19页 |
| 0.1 Variational principles | 第11页 |
| 0.2 Multifractal analysis | 第11-15页 |
| 0.3 Bowen topological entropy for actions of countable discrete groups | 第15-19页 |
| Chapter 1 The Pressure of the Historic Set for Maps with Almost WeakSpecification Property | 第19-31页 |
| 1.1 Preliminaries and main result | 第19-20页 |
| 1.2 Proof of main result | 第20-27页 |
| 1.2.1 Construction of the fractal F | 第21-23页 |
| 1.2.2 Construction of a special sequence of measures μ_k | 第23-27页 |
| 1.3 Modification to obtain Theorem 1.1.1 | 第27-29页 |
| 1.4 Some applications | 第29-31页 |
| Chapter 2 Generic property of the Historic Set for Maps with AlmostWeak Specification Property | 第31-38页 |
| 2.1 Main result | 第31页 |
| 2.2 Proof of main result | 第31-36页 |
| 2.3 Some applications | 第36-38页 |
| Chapter 3 A Variational Principle of Topological Pressure for Maps withAlmost Weak Specification Property | 第38-55页 |
| 3.1 Main result | 第38页 |
| 3.2 Proof of main result | 第38-53页 |
| 3.2.1 Upper bound on P(X(φ,U),ψ) | 第38-39页 |
| 3.2.2 Lower bound on P(X(φ,U),ψ) | 第39-53页 |
| 3.3 Some applications | 第53-55页 |
| Chapter 4 Multifractal Analysis for Maps with the Gluing Orbit Property | 第55-69页 |
| 4.1 Preliminaries and main result | 第55-56页 |
| 4.2 Proof of main result | 第56-69页 |
| 4.2.1 Upper bound on h_(top)~B (X (φ,α)) | 第57页 |
| 4.2.2 Lower bound on h_(top)~B(X(φ，α)) | 第57-69页 |
| Chapter 5 Bowen Topological Entropy for Actions of Countable DiscreteGroups | 第69-92页 |
| 5.1 Main results | 第69-70页 |
| 5.2 Proof of Theorem 5.1.1 | 第70-82页 |
| 5.2.1 A family of Caratheodory dimension structures | 第70-72页 |
| 5.2.2 Lower and upper dimensions of a Borel probability measure | 第72-73页 |
| 5.2.3 Weighted measures and Frostman's lemma | 第73-80页 |
| 5.2.4 Proof of Theorem 5.1.2 | 第80-81页 |
| 5.2.5 Proof of Theorem 5.1.1 | 第81-82页 |
| 5.3 Packing measure and dimension | 第82-89页 |
| 5.4 Other applications of Theorem 5.1.2 | 第89-92页 |
| Bibliography | 第92-98页 |
| Acknowledgements | 第98-99页 |
| Publications or Accepted Papers | 第99页 |
