# Surjunctivity and topological rigidity of algebraic dynamical systems

## TL;DR

This paper investigates conditions under which algebraic dynamical systems on compact metrizable groups are surjunctive, meaning injective equivariant maps are necessarily surjective, contributing to understanding their rigidity properties.

## Contribution

It provides new sufficient conditions for surjunctivity in algebraic dynamical systems with group automorphisms, enhancing the understanding of their topological rigidity.

## Key findings

- Identifies conditions ensuring surjunctivity of algebraic dynamical systems
- Establishes links between algebraic properties and dynamical rigidity
- Advances the theory of topological automorphisms in group actions

## Abstract

Let $X$ be a compact metrizable group and $\Gamma$ a countable group acting on $X$ by continuous group automorphisms. We give sufficient conditions under which the dynamical system $(X,\Gamma)$ is surjunctive, i.e., every injective continuous map $\tau \colon X \to X$ commuting with the action of $\Gamma$ is surjective.