EVENT DETAILS AND ABSTRACT

Title: Zero entropy symbolic dynamical systems
Speaker: Van Cyr
Speaker Info: Bucknell University
Brief Description: second talk of three
Special Note:
Abstract:

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.

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.