# Closing Lemma for Diffeomorphism (Dynamical Systems)

**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

## Bibliography

Dynamics beyond uniform hyperbolicity :\Springer [Encyclopaedia of Mathematical Sciences Volume 102, Mathematical Phisics,2005]

* indicates original appearance(s) of problem.