Graduate Student Seminar-Symbolic Dynamical Systems & their Properties

Date and Time: Tuesday, April 19, 1-2pm

Place: Zoom
Zoom link:https://gwu-edu.zoom.us/j/92957649236?pwd=YmZIYytSUVVwcU1RdjZHYkNFak10U…

Speaker:  Arturu Rodriguez Ramirez, GWU

Title: Symbolic Dynamical Systems & their Properties

Abstract: A dynamical system is a space coupled with a rule to transform the configuration of that space over time, The canonical symbolic dynamical system consists of a space of sequences of symbols, known as words and letters respectively, that are transformed by shifting the position of the origin in each word over time. That space is discrete and compact, and the transformation continuous. By means of an easy to visualize simple finite example and some common infinite examples we introduce and illustrate a number of the topological and measure theoretic properties of interest in dynamical systems in the context of symbolic systems. These include periodic orbits, minimality, transitivity, mixing, entropy, invariant measures, and ergodicity. And we introduce the class of symbolic dynamical systems known as random substitution subshifts.