# Characteristic measures of symbolic dynamical systems

## TL;DR

This paper investigates characteristic measures in symbolic dynamical systems, demonstrating that zero entropy shifts always have such measures and that their automorphism groups are sofic, revealing structural properties of these systems.

## Contribution

It introduces the concept of characteristic measures in symbolic dynamics and proves their existence for zero entropy shifts, also analyzing the nature of their automorphism groups.

## Key findings

- Zero entropy shifts always admit characteristic measures.
- Automorphism groups of minimal zero entropy shifts are sofic.
- Provides new insights into the structure of symbolic dynamical systems.

## Abstract

A probability measure is a characteristic measure of a topological dynamical system if it is invariant to the automorphism group of the system. We show that zero entropy shifts always admit characteristic measures. We use similar techniques to show that automorphism groups of minimal zero entropy shifts are sofic.