英文文摘
Chapter1Introduction
1.1 Preliminary of complex dynamics
1.3 Iterated Function Systems and related
Chapter2 Non-recurrent rational maps
2.1 Non-recurrent rational maps
2.1.1 Background materials
2.1.2 Proofs of main results
2.2 Buried points of Julia set
2.2.1 Bureid points and Lakes of Wada continuum
2.2.2 Buried components of a Julia set
Chapter3 On the connectivity of the Julia set of a rinitely generated rational semigroup
3.1 Some basics
3.2 The connectivity of Julia set
Chapter4 Iterated Function Systems and related
4.1 Perfectness of attractors
4.2 Self-similar sets
4.2.1 Uniform perfectness of X
4.2.2 Hausdorff dimension of self-similar sets
4.3 Self-affine sets
4.3.1 Properties of affine maps
4.3.2 Proof of the main theorem
4.4 The attractor of C1+α bi-Lipschitz IFS on R
4.4.1 Uniform perfectness
4.4.2 C1 Counterexample
4.5 Counting the number of the complement of an components
Bibliography
致谢
博士期间发表的学术论文清单
博士后期间发表的学术论文清单
个人简历
附博士后期间文章
APPLICATIONS OF MANE’S THEOREM
BURIED COMPONENTS OF A JULIA SET
BURIED POINTS AND LAKES OF WADA CONTINUA
GEOMETRY AND DIMENSION OF SELF-SIMILAR SET
UNIFORM PERFECTNESS OF SELF-AFFINE SETS
