Definition:Topological Dynamical System

Definition

Let $\struct {S, \tau}$ be a topological space.

Let $f: S \to S$ be a continuous mapping.

Then $\struct {S, f}$ is called a topological dynamical system.

Also known as

More shortly, $f: S \to S$ is called a topological dynamical system.

Sources

• 2002: Michael Brin and Garrett Stuck: Introduction to Dynamical Systems Chapter $2$: Topological Dynamics