Measures of maximal entropy of bounded density shifts

TL;DR

This paper establishes conditions under which bounded density shifts have unique, fully supported measures of maximal entropy, and demonstrates that such shifts are surjunctive, contributing to the understanding of their dynamical properties.

Contribution

It provides new sufficient conditions for uniqueness and support of measures of maximal entropy in bounded density shifts, and proves their surjunctivity.

Findings

Bounded density shifts have unique measures of maximal entropy under certain conditions.

All measures of maximal entropy in these shifts are fully supported.

Bounded density shifts are surjunctive.

Abstract

We find sufficient conditions for bounded density shifts to have a unique measure of maximal entropy. We also prove that every measure of maximal entropy of a bounded density shift is fully supported. As a consequence of this, we obtain that bounded density shifts are surjunctive.