题目：Upper semi-continuity of entropy map for non-uniformly hyperbolic systems   

报告人：王式柔博士  北京大学

报告时间：2016年6月21日下午2：00-3：00
         
报告地点：数学楼二楼学术报告厅
         
摘要：For a continuous transformation f on a compact manifold M, the entropy map of f is defined by the metric entropy on the set of all f-invariant measures and it is generally not continuous. However, it is still worth our effort to investigate the upper semi-continuity of it since, for instance, it implies the existence of invariant measures of maximal entropy. In this talk I will talk about the upper semi-continuity of entropy map for non-uniformly hyperbolic systems. Firstly, we prove that for C1 non-uniformly hyperbolic systems with domination, the entropy map is upper semi-continuous; then we give a counter example showing that this is not necessarily true for C1+r non-uniformly hyperbolic systems without domination. This goes a little against a common intuition that conclusions are parallel between this two kinds of non-uniformly hyperbolic systems. This is a joint work with Gang Liao and Wenxiang Sun.