Title: Zero entropy symbolic dynamical systems
Speaker: Van Cyr
Speaker Info: Bucknell University
Brief Description: Third talk of three
Symbolic dynamics is the study of the left-shift map acting on various closed subsets of the space of allA-colorings of the integers, where A is a finite alphabet). At first blush these systems seem simple, but looks can be deceiving: the famous Jewett-Krieger theorem states that any ergodic, probability-preserving dynamical system with finite entropy is (measure-theoretically) isomorphic to a subshift. Even as purely topological systems, subshifts provide examples that exhibit much of the richness of general systems while also being explicit enough for important problems to be tractable.Date: Thursday, November 5, 2015
In these lectures, I will survey some of the main theorems and open problems about symbolic dynamics with a focus on the study of systems with zero topological entropy. The first lecture will introduce the audience to the group of automorphisms of a symbolic system in one (or more) dimensions. The second lecture will survey some recent advances in the study of automorphisms of one-dimensional systems of zero entropy. The third lecture will study the ergodic properties of low complexity subshifts.