Multifractal analysis of non-uniformly contracting iterated function systems

报告时间：10月10日（星期二）上午11：00-11:30

报告地点：数学实验室(工北412)

报告摘要：Let $X = [0, 1]$. Given a non-uniformly contracting conformal iterated function system (IFS) $\{ w_j \}_{j = 1}^m$ and a family of positive Dini continuous potential functions $\{ p_j \}_{j=1}^m$, the triple system $(X, \{w_j\}_{j=1}^m, \{p_j\}_{j=1}^m)$, under some conditions, determines uniquely a probability invariant measure, denoted by $\mu$. In this paper, we study pressure function of the system and multifractal structure of $\mu$. We prove that the pressure function is Gateaux differentiable and the multifractal formalism holds, if the IFS $\{ w_j \}_{j = 1}^m$ has non-overlapping.

报告人简介：叶远灵：华南师范大学 数学科学学院教授、博士生导师，香港中文大学博士。主要研究领域为：动力系统，分形几何，泛函分折。