| 摘要 | 第8-9页 |
| Abstract | 第9页 |
| Preface | 第10-20页 |
| 0.1 Metric Diophantine approximation | 第12-14页 |
| 0.2 Nondense orbit set | 第14-15页 |
| 0.3 Multifractal analysis | 第15-20页 |
| Chapter 1 Quantitative recurrence properties for free semigroup actions | 第20-28页 |
| 1.1 Preliminaries and main results | 第20-23页 |
| 1.2 Proof of Theorem 1.1.4 and 1.1.5 | 第23-28页 |
| Chapter 2 Quantitative recurrence properties for systems with non-uniformstructure | 第28-46页 |
| 2.1 Preliminaries and main results | 第28-32页 |
| 2.1.1 Topological pressure | 第30-32页 |
| 2.2 Proof of Theorem 2.1.1 | 第32-39页 |
| 2.2.1 Proof of upper bound | 第33-34页 |
| 2.2.2 Proof of lower bound | 第34-39页 |
| 2.3 Proof of Theorem 2.1.2 | 第39-45页 |
| 2.3.1 Proof of upper bound | 第39-40页 |
| 2.3.2 Proof of lower bound | 第40-45页 |
| 2.4 Applications | 第45-46页 |
| Chapter 3 Topological pressure of generic points sets with non-unifromstructure | 第46-61页 |
| 3.1 Preliminaries and main results | 第46-49页 |
| 3.2 Proof of Theorem 3.1.2 | 第49-59页 |
| 3.2.1 Choose the sequence {n_j}_(j≥1) | 第50-51页 |
| 3.2.2 Construction of fractal set H | 第51-56页 |
| 3.2.3 To estimate the lower bound | 第56-59页 |
| 3.3 Applications | 第59-61页 |
| Chapter 4 Quantitative recurrence properties in the historic set for sym-bolic systems | 第61-84页 |
| 4.1 Preliminaries and main results | 第61-65页 |
| 4.2 Some important lemmas | 第65-67页 |
| 4.3 Proof of Theorem 4.1.1 | 第67-74页 |
| 4.3.1 Proof of upper bound | 第67-68页 |
| 4.3.2 Proof of lower bound | 第68-74页 |
| 4.4 Proof of Theorem 4.1.2 | 第74-84页 |
| 4.4.1 Proof of upper bound | 第74-75页 |
| 4.4.2 Proof of lower bound | 第75-84页 |
| Chapter 5 On the topological entropy of the set with a special shadowingtime | 第84-107页 |
| 5.1 Preliminaries and main results | 第84-87页 |
| 5.2 Proof of Theorem 5.1.2 | 第87-105页 |
| 5.2.1 Upper bound for h_(top)~B(D_f~(xo)) | 第87-89页 |
| 5.2.2 Lower bound for h_(top)~B(D_f~(xo)) | 第89-91页 |
| 5.2.3 Construction of the Fractal F | 第91-95页 |
| 5.2.4 Construction of a special sequence of measure μ_k | 第95-105页 |
| 5.3 Applications | 第105-107页 |
| Chapter 6 Non-dense orbits on topological dynamical systems | 第107-116页 |
| 6.1 Preliminaries and main results | 第107页 |
| 6.2 Proof of Theorem 6.1.1 | 第107-113页 |
| 6.2.1 Construction of the Fractal F | 第108-110页 |
| 6.2.2 Construction of a special sequence of measures μ)k | 第110-113页 |
| 6.3 Applications | 第113-116页 |
| Bibliography | 第116-121页 |
| Acknowledgements | 第121-122页 |
| Publications and Preprints | 第122-123页 |
| Further researches | 第123页 |
