Absolutely Continuous Invariant Measure for Generalized Horseshoe Maps

TL;DR

This paper proves that under certain conditions, the SRB measures of generalized horseshoe maps are absolutely continuous with respect to Lebesgue measure, enhancing understanding of their statistical properties.

Contribution

It establishes conditions under which SRB measures for generalized horseshoe maps are absolutely continuous, providing new insights into their measure-theoretic behavior.

Findings

SRB measures are absolutely continuous under transversality and fatness conditions

The results apply to a broad class of generalized horseshoe maps

Enhances understanding of statistical properties of chaotic dynamical systems

Abstract

In this paper, we study the SRB measures of generalized horseshoe map. We prove that under the conditions of transversality and fatness, the SRB measure is actually absolutely continuous with respect to the Lebesgue measure.