**Title:** Zero entropy symbolic dynamical systems

**Speaker:** Van Cyr

**Speaker Info:** Bucknell University

**Brief Description:** Third 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.

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