Problem Sheet D

This Problem Sheet is based on Lectures 7 and 8.

• Problem 1 shows that having zero topological entropy is an inheritable property.
• Problem 2 shows that topological entropy behaves nicely under iteration.
• Problem 3 asks you to prove that reversible dynamical systems on an interval have zero topological entropy.
• Problem 4 asks you to show that hyperbolic toral automorphisms are always mixing.
• Problem 5 on the other hand shows that toral automorphisms that are not hyperbolic are as far away from being mixing as possible.