Maximal entropy measures for Viana maps

TL;DR

This paper constructs measures of maximal entropy for Viana maps, a class of dynamical systems with critical points, using their non-uniform expansion and slow recurrence properties.

Contribution

It introduces a method to establish maximal entropy measures for Viana maps based on their non-uniform hyperbolic behavior.

Findings

Existence of measures of maximal entropy for Viana maps.

Utilization of non-uniform expansion and slow recurrence in the proof.

Extension of entropy theory to maps with critical points.

Abstract

In this note we construct measures of maximal entropy for a certain class of maps with critical points called Viana maps. The main ingredients of the proof are the non-uniform expansion features and the slow recurrence (to the critical set) of generic points with respect to the natural candidates for attaining the topological entropy.