Statistical stability and continuity of SRB entropy for systems with Gibbs-Markov structures

TL;DR

This paper establishes conditions under which SRB entropy remains stable and continuous for certain dynamical systems with Gibbs-Markov structures, with applications to Henon maps.

Contribution

It introduces new criteria for statistical stability and SRB entropy continuity based on horseshoe-like sets with variable return times.

Findings

Conditions for statistical stability and entropy continuity are identified.

Application to Henon maps within Benedicks-Carleson parameters demonstrates the theory.

Provides a framework for analyzing stability in complex dynamical systems.

Abstract

We present conditions on families of diffeomorphisms that guarantee statistical stability and SRB entropy continuity. They rely on the existence of horseshoe-like sets with infinitely many branches and variable return times. As an application we consider the family of Henon maps within the set of Benedicks-Carleson parameters.