Description:

Title: The Stabilized Automorphism Group of Minimal Systems

Abstract: The stabilized automorphism group of a dynamical system (X, T ) is the group of all self-homeomorphisms of X that commute with some power of T. In this talk, we will describe the stabilized automorphism group of minimal systems. Our approach will involve utilizing algebraic tools in a novel way to extract information about the rational eigenvalues of these systems from their stabilized automorphism groups. 

We'll begin by characterizing the stabilized automorphism groups for odometers and Toeplitz subshifts. We'll then demonstrate an invariance property of the stabilized automorphism groups for these systems. Additionally, we'll extend these results to a broader class of systems and show that if two minimal systems have isomorphic stabilized automorphism groups, and each has at least one non-trivial rational eigenvalue, then they share the same rational eigenvalues. Furthermore, we'll extend a known result on mixing shifts of finite type to apply to irreducible shifts of finite type.