Existence of SRB measures for hyperbolic maps with weak regularity

Abstract

We prove that a $C^1$ hyperbolic map whose differential is regular enough has an SRB measure. The precise regularity condition is weaker than Hölder and was mentioned by various authors through the development of expanding and uniformly hyperbolic dynamics.

Keywords:

• Hyperbolic dynamics
• weak regularity
• modulus of continuity

Disclosure statement

No potential conflict of interest was reported by the author(s).