Cr-Closing lemma for partially hyperbolic diffeomorphisms on 3-manifolds

主讲人：史逸 北京大学 研究员

时间：2019年4月15日11：15

地点：徐汇校区三号楼332

举办单位：数理学院

内容介绍：The Cr-closing lemma is one well-known problem in the theory of dynamical  systems. The problem is to perturb the original dynamical system so as to obtain  a Cr-close system that has a periodic orbit passing through a given point. And  this point is called Cr-closable. In this talk, we prove the Cr-closing lemma (r  = 2,3,···,∞) for partially hyperbolic diffeomorphisms on 3-manifolds: every  non-wandering point of these diffeomorphisms is Cr-closable. Moreover, we will  show that Cr-generic conservative partially hyperbolic diffeomorphisms on  3-manifolds have dense periodic points.This is a joint work with Shaobo Gan.