| 摘要 | 第1-9页 |
| Abstract | 第9-10页 |
| Prefaces | 第10-20页 |
| Chapter 1 Local Topological Pressure for Sofic Groups Actions | 第20-30页 |
| ·Preliminaries | 第20-23页 |
| ·Variational Principle for Sofic Local Topological Pressure | 第23-28页 |
| ·Properties of Sofic Local Topological Pressure | 第28-30页 |
| Chapter 2 Topological Pressure for Sofic Groupoids Actions | 第30-52页 |
| ·Preliminaries | 第30-33页 |
| ·Discrete Groupoid | 第30-32页 |
| ·Sofic Approximations,Actions,Spanning and Separating Sets | 第32-33页 |
| ·Topological Pressure for Sofic Groupoids | 第33-42页 |
| ·Measure Entropy | 第42-45页 |
| ·Variational Principle | 第45-52页 |
| Chapter 3 Multifractal Analysis for the Historic Set | 第52-78页 |
| ·Preliminaries | 第53-57页 |
| ·Upper and Lower Bounds forP(G_(k')~*,φ) | 第57-64页 |
| ·Proofs of Theorems | 第64-68页 |
| ·Some Applications | 第68-78页 |
| ·Some Spectra | 第68-73页 |
| ·The Relative Multifractal Spectrum of Ergodic Averages | 第73-75页 |
| ·Symbolic Spaces and Iterated Function Systems | 第75-78页 |
| Chapter 4 Packing Entropy and Historic Set | 第78-93页 |
| ·Preliminaries | 第78-80页 |
| ·Proof of Theorem 4.0.1 | 第80-91页 |
| ·Construction of the Intermediate Sets {C_k}_(κ∈N\{O}) | 第82-83页 |
| ·Construction of the Intermediate Sets {L_k}_(κ∈N\{O}) | 第83页 |
| ·Construction of the Fractal Z and a Special Sequence of Measuresμk | 第83-91页 |
| ·Examples | 第91-93页 |
| Chapter 5 Topological Pressure of Strong Scrambled Sets | 第93-117页 |
| ·Preliminaries | 第93-94页 |
| ·A Moran Fractal F with Full Topological Pressure | 第94-105页 |
| ·Construction of a Strong Scrambled Set W | 第105-108页 |
| ·A Strong Scrambled Set with Full Topological Pressure | 第108-112页 |
| ·A Strong Scrambled Set C with Full Topological Pressure Everywhere | 第112-115页 |
| ·Applications | 第115-117页 |
| Chapter 6 Strong Scrambled Sets in the Multifractal Structure | 第117-134页 |
| ·Construction of Basic Sets S_k | 第117-119页 |
| ·Intermediate Sets {D_k}_(κ∈N) and {L_k}_(κ∈N) | 第119-121页 |
| ·Construction of the Moran Fractal F and a Special Sequence of Measures μ_k | 第121-123页 |
| ·Construction of a Strong Scrambled Set W | 第123-126页 |
| ·A Strong Scrambled Set△(F) (?) X(Φ,α)with the Same Topological Pressure as X(Φ,α) | 第126-132页 |
| ·Applications | 第132-134页 |
| Chapter 7 Packing Dimensions and the Self-similar Measures | 第134-145页 |
| ·Preliminaries | 第135-137页 |
| ·Proof of Theorem 7.0.2 | 第137-145页 |
| ·Proof of Inequality 7.2.1 | 第137-142页 |
| ·Proof of Inequality 7.2.2 | 第142-145页 |
| Bibliography | 第145-151页 |
| Acknowledgements | 第151-153页 |
| Further researches | 第153-154页 |
| Publications or Accepted Papers | 第154页 |
