Title:Closing lemma for partially hyperbolic diffeomorphisms on 3-manifolds
Speaker: Yi Shi (Peking University)
Abstract: The-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 -close system that has a periodic orbit passing through a given point. And this point is called -closable. Steve Smale listed the -closing lemma as one of mathematical problems for this century.
In this talk, we prove theclosing lemma for partially hyperbolic diffeomorphisms on 3-manifolds: every non-wandering point of these diffeomorphisms is -closable. Moreover, we will show that -generic conservative partially hyperbolic diffeomorphisms on 3-manifolds have dense periodic points.