Modulus of continuity of invariant densities and entropies for piecewise expanding maps

TL;DR

This paper provides quantitative estimates on how invariant densities and entropies change continuously for certain families of piecewise expanding maps, including applications to two-dimensional tent maps.

Contribution

It extends existing perturbation results to quantify the continuity of invariant measures and entropies in piecewise expanding maps, with specific application to 2D tent maps.

Findings

Quantitative bounds on the continuity of invariant densities.

Quantitative bounds on the continuity of entropies.

Application to two-dimensional tent maps.

Abstract

Using a perturbation result established by Galatolo and Lucena, we obtain quantitative estimates on the continuity of the invariant densities and entropies of the physical measures for some families of piecewise expanding maps. We apply these results to a family of two-dimensional tent maps.