| Abstract in Chinese | 第1-6页 |
| Abstract in English | 第6-7页 |
| Chapter 0 Preliminaries | 第7-10页 |
| Chapter 1 Self-conformal sets in complete metric spaces | 第10-35页 |
| 1．1 Notations and definitions | 第10-12页 |
| 1．2 Basic properties of a conformal iterated function system | 第12-21页 |
| 1．3 Self-conformal sets in complete metric spaces | 第21-35页 |
| Chapter 2 Problems on graph-directed iterated function systems | 第35-55页 |
| 2．1 Graph-directed iterated function systems | 第35-36页 |
| 2．2 Equivalence of positive Hausdorff measure and the open set condition for graph-directed self-conformal sets | 第36-47页 |
| 2．2．1 Graph-directed self-conformal sets | 第36-40页 |
| 2．2．2 The proof of the equivalence theorem | 第40-47页 |
| 2．3 A measure dimension estimate for a graph-directed iterated function system of non-similarities | 第47-55页 |
| 2．3．1 Measure's dimension and main results | 第47-49页 |
| 2．3．2 The measure dimension estimate | 第49-55页 |
| Chapter 3 Topological entropy of the set of divergence points | 第55-90页 |
| 3．1 Introduction and definitions | 第55-62页 |
| 3．1．1 Background of multifractal analysis | 第55-57页 |
| 3．1．2 Topological entropy of non-compact sets | 第57-59页 |
| 3．1．3 Specification property and deformation of measures | 第59-62页 |
| 3．2 Topological entropy of sup sets | 第62-75页 |
| 3．3 Topological entropy of the set of divergence points | 第75-90页 |
| References | 第90-91页 |
