Topological entropy for automorphisms of totally disconnected locally compact groups

TL;DR

This paper introduces a simplified formula for calculating topological entropy of automorphisms in totally disconnected locally compact groups, extending known properties from compact groups to a broader class.

Contribution

It provides a limit-free formula that simplifies entropy computation and extends fundamental properties to a wider class of groups.

Findings

Derived a limit-free formula for topological entropy

Extended properties of entropy from compact to locally compact groups

Simplified entropy calculations for automorphisms

Abstract

We give a "limit-free formula" simplifying the computation of the topological entropy for topological automorphisms of totally disconnected locally compact groups. This result allows us to extend several basic properties of the topological entropy known to hold for compact groups.