Introduction to Bratteli Diagrams and Bounded Topological Speedups

Abstract: Given a dynamical system $(X,T)$, one can define a speedup of $(X,T)$ as another dynamical system $S: X → X$ where $S= T^{p(·)}$ for some $p: X → Z^+$. In this talk, we will focus on bounded topological speedups of minimal Cantor systems. Specifically, we require that our “jump function” $p$ be bounded and hence continuous. Our motivating question is: What, if anything, can be preserved with the added structure of p being bounded? To do so, we introduce Kakutani-Rokhlin towers and Bratteli diagrams as ways of visualizing the dynamics of minimal Cantor systems. Then we will illustrate a novel construction of a Bratteli diagram for $(X,S)$ given a Bratteli diagram for $(X,T)$. We will conclude the talk with an brief application of this constructions as well as discuss various open problems inspired by this construction. The work presented is joint work with Andrew Dykstra and Michelle LeMasurier, both of Hamilton College.

dynamical systems

Audience: researchers in the topic

Little school dynamics

Series comments: Email dynamics@aimath.org to ask for the Zoom link.