报告题目： A criterion ensuring the ergodicity of the limit of periodic measures


报告人 张金华（北京大学）


报告时间 2017年7月18日15:30-16:30

报告地点  维格堂319

报告摘要 In this talk, we will review a criterion by  Gorodetski-Ilyashenko-Kleptsyn-Nalsky which ensures the ergodicity of the limit of periodic measures.
This criterion was first designed to obtain non-hyperbolic ergodic measures for generic diffeomorphisms.


报告题目：Existence of non-hyperbolic ergodic measures obtained by the limit of periodic measures

报告人 张金华（北京大学）


报告时间 2017年7月18日16:30-17:30

报告地点  维格堂319

报告摘要 In this talk, in a semi-local setting, we will  show that for the set of diffeomorphisms having robust cycles, there exists an open dense  subset of diffeomorphisms exhibiting non-hyperbolic ergodic measures obtained by the limit of periodic measures. Furthermore, we show that open and dense in the set of robustly transitive and non-hyperbolic diffeomorphisms  far from homoclinic tangencies, there exist non-hyperbolic ergodic measures with full support. This is a joint work with Christian Bonatti

报告题目：Ergodic measures with multi-zero center Lyapunov exponent

报告人 张金华（北京大学）


报告时间 2017年7月18日17:30-18:30

报告地点  维格堂319

报告摘要 To some extent, the non-hyperbolicity can be characterized by the existence of nonhyperbolic ergodic measures, and the number of vanishing Lyapunov exponents describes how far from hyperbolicity the systems are. In this talk, we will show that for C1-generic diffeomorphisms, if a homoclinic class contains periodic orbits of indices i and j with j > i + 1, and the homoclinic class has no-domination of index l for any l ∈ {i + 1,··· ,j −1}, then there exists a non-hyperbolic ergodic measure with more than one vanishing Lyapunov exponents and whose support is the whole homoclinic class. This is a joint work with Xiaodong WANG.