MTH-212.4 Symbolic Dynamics

Consider all words in the symbols 0 and 1 such that no two 1s sit adjacent to one another. Can you calculate the asymptotic growth rate of the number of words of length n? This elementary question is related to an important invariant called the topological entropy for certain automorphisms of the torus. The study of such questions arises in the field of symbolic dynamics which is an essential section of ergodic theory and coding theory. In this course we will study symbolic dynamics on the group Z.

For most of the course we will focus on the elementary symbolic dynamics. There after we will branch out to two specific applications: Into coding theory and to topological dynamics. We will follow the book Introduction to Symbolic Dynamics and Coding by Brian Marcus and Douglas Lind for most of the course.