题目： The folding type Ruelle inequality
报告人： 王式柔 (University of Alberta)
时间：2018年7月1日 9：00-10：00
摘要：In dynamical systems, the classical Ruelle inequality tells us that the metric entropy is dominated by the sum of positive Lyapunov exponents. In this talk, I will talk about a folding type Ruelle inequality, which looks at the system from backward process.
题目： An Application of folding type inequality--- Upper semi-continuity of metric entropy
报告人： 王式柔 (University of Alberta)
时间：2018年7月1日 10：00-11：00
摘要：As an application of folding type inequality introduced in the first part of the talk, I will introduce the notion of folding rate and give a sufficient condition of upper semi-continuity of metric entropy for interval or circle maps.
题目： A counter example---the sharpness of the condition of uniform folding rate
报告人： 王式柔 (University of Alberta)
时间：2018年7月1日 11：00-12：00
摘要：I will talk about an example of interval map for which an ergodic measure with positive entropy is not an upper semi-continuity point of metric entropy. This ergodic measure is approximated by a sequence of invariant measures without uniform folding rate, which implies that the condition of uniform folding rate in the second part of the talk is sharp. Also, this gives a negative answer to the question that whether ergodic measure with positive entropy is an upper semi-continuity point of metric entropy.