Strong orbit equivalence and automorphism group of minimal cantor systems

SEMINAR TALK

Title: Strong orbit equivalence and automorphism group of minimal cantor systems

Abstract: Two topological dynamical systems are said to be orbit equivalent if there exists a homeomor phism from one state space to another that induces a bijective correspondence between their orbits. Building on the celebrated result of Giordano, Putnam, and Skau, which completely describes the orbit (or strong orbit) equivalence of minimal Cantor systems, several works have been done on characterizing the dynamical invariants in this context.

This talk aims to introduce one such dynamical invariant - the automorphism group within strong orbit equivalence classes. We illustrate that within any given strong orbit equivalence class of minimal Cantor systems, one can always find dynamical systems of zero entropy whose automorphism group is isomorphic to Z. We use the concept of asymptoticity and tools from symbolic dynamics to obtain systems of this property.

This talk is based on joint work with Sebasti ́an Donoso.