Intrinsic ergodicity via obstruction entropies

TL;DR

This paper extends Bowen's result by demonstrating that a unique measure of maximal entropy exists under weaker conditions than expansivity and specification, using obstruction entropies to characterize these conditions.

Contribution

It introduces the concepts of obstructions to expansivity and specification and establishes uniqueness of the measure of maximal entropy when their entropy is sufficiently small.

Findings

Unique measure of maximal entropy under weaker conditions

Obstructions to expansivity and specification are characterized by their entropy

The entropy of obstructions being less than topological entropy guarantees uniqueness

Abstract

Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions of these hypotheses. To this end, we introduce the notions of obstructions to expansivity and specification, and show that if the entropy of such obstructions is smaller than the topological entropy of the map, then there is a unique measure of maximal entropy.