报告题目：Multifractal analysis of non-uniformly contracting iterated function systems

报 告 人：叶远灵教授（华南师范大学）

报告时间：2019年11月16日 15:00-16:00

报告地点：数统院303学术报告厅

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.