Existence of SRB measures for hyperbolic maps with weak regularity

TL;DR

This paper proves the existence of SRB measures for certain hyperbolic maps with regularity conditions weaker than H{"o}lder, expanding understanding of invariant measures in dynamical systems.

Contribution

It establishes the existence of SRB measures for $C^1$ hyperbolic maps under weaker regularity conditions than previously known.

Findings

SRB measures exist for a class of $C^1$ hyperbolic maps with weak regularity

Regularity condition weaker than H{"o}lder is sufficient for SRB measure existence

Advances the theory of invariant measures in hyperbolic dynamics

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 H{\"o}lder and was mentionned by various authors through the developement of expanding and uniformly hyperbolic dynamics.