Abstract :

Symbolic dynamics is a tool for analyzing general dynamical systems by discretizing space. Recall that, a set of infinite words over an alphabet $A$ is a shift space if it is closed with respect to the natural product topology of $A^N$ and invariant under the shift operator. In this talk, first we will introduce sub shifts of finite type and then will discuss symbolic dynamics, the process of modeling a topological or smooth dynamical system by a discrete space with the dynamics given by the shift operator. Some applications of symbolic dynamics shall be discussed.