Entropy formula for C1 expanding maps

TL;DR

This paper proves that pseudo-physical measures of C1 expanding maps on compact manifolds satisfy Pesin's entropy formula, including examples on the circle and 2-torus.

Contribution

It establishes the Pesin entropy formula for pseudo-physical measures in C1 expanding dynamical systems, extending previous results beyond smoother classes.

Findings

Pseudo-physical measures satisfy Pesin entropy formula.

Includes examples of C1 expanding maps on circle and 2-torus.

Studies properties of pseudo-physical measures in non C1 plus Holder maps.

Abstract

We prove that the (necessarily existing) pseudo-physical or SRB-like measures of C1 expanding dynamical systems on a compact Riemannian manifold satisfy Pesin entropy formula. We include examples of C1 (non C1 plus Holder) expanding maps on the circle and on the 2 torus and study their pseudo-physical measures.