# 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.

Comments and questions?