报告题目： Ergodicity and partial hyperbolicity


报告人  Rodriguez-Hertz, M.（南方科技大学）



报告时间 2017年2月22日09:30-11:30


报告地点  维格堂319


报告摘要   The mark and recapture method is used in ethology and epidemiology among other applications. 

We show how this method is one of the possible uses of ergodicity and stable ergodicity. 
We show how partial hyperbolicity is related to ergodicity and present some related open problems.




报告题目：Ergodicity in low differentiability


报告人  Rodriguez-Hertz, M.（南方科技大学）



报告时间 2017年2月23日09:30-11:30


报告地点  维格堂319


报告摘要   As we have seen, ergodicity is a hypothesis that is used in many applications. 

How frequent is ergodicity among systems? This depends on our definition of frequency. 
It is known that among homeomorphisms, ergodicity is dense, and hence generic. 
On the other hand, KAM-phenomenon shows that there is a C^3-open set of non-ergodic 
diffeomorphisms. What about the intermediate topologies? We present a panoramic view

of results and open questions. 

报告题目： Structure of accessibility classes for center dimension 2报告人  Rodriguez-Hertz, M.（南方科技大学）报告时间 2017年2月24日10:00-12:00报告地点  维格堂319报告摘要    For partially hyperbolic diffeomorphisms, the accessibility class of a point is the set of pointsthat can be reached from this point by means of a finite concatenation of stable and unstable arcs. If there is only one accessibility class, the system is said to be accessible. In the case of one-dimensional center bundle, it is known that accessibility classes are either codimension-one immersed manifolds, or open sets. Also, that accessibility is a $C^1$ open property. In a joint work with Carlos Vasquez, we show that this results hold for partially hyperbolic diffeomorphisms with two-dimensional center bundle. However, the denseness of accessibility remainsan open problem.