Dirac physical measures for generic diffeomorphisms

ABSTRACT

We prove that, for a C¹ generic diffeomorphism, the only Dirac physical measures with dense statistical basin are those supported on sinks.

KEYWORDS:

• Generic diffeomorphisms
• physical measures

MSC 2010 classification::

• 37C05
• 37C20
• 37D30

Acknowledgments

I thank Pablo Guarino for many useful discussions and for his comments on a preliminary version of this paper. The anonymous referee made also many useful comments which helped to improve the paper. I thank him/her.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. See for instance [21].