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Abstract in Chinese |
5-6 |
|
Abstract in English |
6-7 |
|
Chapter 0 Preliminaries |
7-10 |
|
Chapter 1 Self-conformal sets in complete metric spaces |
10-35 |
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1．1 Notations and definitions |
10-12 |
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1．2 Basic properties of a conformal iterated function system |
12-21 |
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1．3 Self-conformal sets in complete metric spaces |
21-35 |
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Chapter 2 Problems on graph-directed iterated function systems |
35-55 |
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2．1 Graph-directed iterated function systems |
35-36 |
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2．2 Equivalence of positive Hausdorff measure and the open set condition for graph-directed self-conformal sets |
36-47 |
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2．2．1 Graph-directed self-conformal sets |
36-40 |
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2．2．2 The proof of the equivalence theorem |
40-47 |
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2．3 A measure dimension estimate for a graph-directed iterated function system of non-similarities |
47-55 |
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2．3．1 Measure's dimension and main results |
47-49 |
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2．3．2 The measure dimension estimate |
49-55 |
|
Chapter 3 Topological entropy of the set of divergence points |
55-90 |
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3．1 Introduction and definitions |
55-62 |
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3．1．1 Background of multifractal analysis |
55-57 |
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3．1．2 Topological entropy of non-compact sets |
57-59 |
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3．1．3 Specification property and deformation of measures |
59-62 |
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3．2 Topological entropy of sup sets |
62-75 |
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3．3 Topological entropy of the set of divergence points |
75-90 |
|
References |
90-91 |
