## Introduction to Symbolic Dynamics

### Content

This is a cycle of seminars on the first five chapters of the book
*An Introduction to Symbolic Dynamics and Coding*
by Douglas Lind and Brian Marcus.

I meant it as a way of learning something by teaching it to others.

### Issues

- First talk: April 7, 2010
- Introduction
- Shift spaces
- Basic constructions on shift spaces
- Sliding block codes
- A parallel with coding theory

- Second talk: April 14, 2010
- Shifts of finite type
- Graphs and their shifts
- Graphs as presentations of shifts
- An application to data recording

- Third talk: April 28, 2010
- State splitting
- Sofic shifts
- Characterization of sofic shifts
- Minimal right-resolving presentation

- Fourth talk: May 12, 2010
- Constructions on sofic shifts
- Entropy of a shift space
- Computing entropy via Perron-Frobenius theory

- Fifth talk: May 19, 2010
- Cyclic structure of irreducible matrices
- Road-colorings and right-closing labelings
- The finite-state coding theorem

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###### Last update: May 19, 2010