In this lecture we start computing the topological entropy of some of our model systems. We begin by showing that any circle rotation has zero entropy. We then show that the doubling map $e_2 \colon S^1 \to S^1$ has entropy $ \log 2$.

We then generalise this to higher-dimensional tori. We define a class of dynamical systems called hyperbolic toral automorphisms and compute their entropy.  

As the name suggests, hyperbolic toral automorphisms are an example of a hyperbolic dynamical system. We will come back to these in Dynamical Systems II.

Comments and questions?