# Dynamics , Pertubation

## Closing Lemma for Diffeomorphism (Dynamical Systems) ★★★★

Author(s): Charles Pugh

**Conjecture**Let and . Then for any neighborhood there is such that is periodic point of

There is an analogous conjecture for flows ( vector fields . In the case of diffeos this was proved by Charles Pugh for . In the case of Flows this has been solved by Sushei Hayahshy for . But in the two cases the problem is wide open for

Keywords: Dynamics , Pertubation