Topological and Ergodic properties of symmetric subshifts

TL;DR

This paper investigates the topological and ergodic properties of symmetric one-sided subshifts over two symbols, revealing that most have a unique measure of maximal entropy and analyzing properties like transitivity and specification.

Contribution

It provides a detailed analysis of the topological and ergodic properties of symmetric subshifts, including conditions for intrinsic ergodicity and measure uniqueness.

Findings

Almost every symmetric subshift admits only one measure of maximal entropy

The paper characterizes transitivity and the specification property in these subshifts

Provides conditions under which these subshifts are intrinsically ergodic

Abstract

The family of symmetric one sided subshifts in two symbols given by a sequence $a$ is studied. We analyse some of their topological properties such as transitivity, the specification property and intrinsic ergodicity. It is shown that almost every member of this family admits only one measure of maximal entropy.