题目: Partially Hyperbolic Dynamics: Classification and Stochastic Description
报告人:张金华（法国巴黎第十一大学）
时间:2018/12/19 14:00-15:30
摘要:Smale’s hyperbolic theory characterizes the dynamics which are (structurally) stable under small perturbations. Nowadays, the dynamics of hyperbolic systems is considered as well understood from topological viewpoint as well as from stochastic viewpoint. However, examples by Smale et al show that hyperbolic dynamics are not dense. One of the main goals is to understand the dynamics beyond uniform hyperbolicity.
In 1970s, Brin-Pesin proposed the notion of partial hyperbolicity to release the no- tion of uniform hyperbolicity. In this talk, I would give some characterization of certain partially hyperbolic dynamics from topological viewpoint and stochastic viewpoint:
(1) I will present that there exists new partially hyperbolic systems which are different from classical ones and give a classification result;
(2) I will give some stochastic description of the asymptotic behavior of typical points on the manifold.
This talk is based on some recent results with C. Bonatti and S. Crovisier–D. Yang respectively