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Ergodic Theory / Probability Seminar - Yi Shi

Ergodic Theory/Probability Seminar
January 17, 2019
3:00PM - 4:00PM
Math Tower 154

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Add to Calendar 2019-01-17 15:00:00 2019-01-17 16:00:00 Ergodic Theory / Probability Seminar - Yi Shi Title: $C^r$ Closing lemma for partially hyperbolic diffeomorphisms on 3-manifolds Speaker: Yi Shi (Peking University) Abstract: The $C^r$-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 $C^r$-close system that has a periodic orbit passing through a given point. And this point is called $C^r$-closable. Steve Smale listed the $C^r$-closing lemma as one of mathematical problems for this century. In this talk, we prove the $C^r (r=2,3,\cdots, \infty)$ closing lemma for partially hyperbolic diffeomorphisms on 3-manifolds: every non-wandering point of these diffeomorphisms is $C^r$-closable. Moreover, we will show that $C^r$-generic conservative partially hyperbolic diffeomorphisms on 3-manifolds have dense periodic points. This is a joint work with Shaobo Gan. Math Tower 154 Department of Mathematics math@osu.edu America/New_York public

Title: $C^r$ Closing lemma for partially hyperbolic diffeomorphisms on 3-manifolds

Speaker: Yi Shi (Peking University)

Abstract: The $C^r$-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 $C^r$-close system that has a periodic orbit passing through a given point. And this point is called $C^r$-closable. Steve Smale listed the $C^r$-closing lemma as one of mathematical problems for this century.

In this talk, we prove the $C^r (r=2,3,\cdots, \infty)$ closing lemma for partially hyperbolic diffeomorphisms on 3-manifolds: every non-wandering point of these diffeomorphisms is $C^r$-closable. Moreover, we will show that $C^r$-generic conservative partially hyperbolic diffeomorphisms on 3-manifolds have dense periodic points.

This is a joint work with Shaobo Gan.

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