South African - Japanese Discrete Homotopy Meeting 2025 (Cape Town, South Africa, 10-11 September 2025)

11th of September 2025  - 10.40/11.20  

Venue: MAM111 - Department of Mathematics and Applied Mathematics - University of Cape Town

Speaker:   Olwethu Waka (University of the Western Cape, Bellville, South Africa)

Title:          Topological entropy of totally disconnected locally compact abelian groups via the mastergraph

Abstract:  The notion of topological entropy is present in many areas of mathematics, but here we are interested in the topological entropy of continuous automorphisms of totally disconnected locally compact abelian groups. Then we explore the notion of mastergraph, which is more recent in the literature and can be associated to these groups. It turns out that appropriate restrictions on the mastergraph imply the presence of continuous automorphisms of finite topological entropy. We show how this is possible with the help of a few examples of well known totally disconnected locally compact abelian groups.