This Problem Sheet is based on Lecture 37.

• Problem 1 asks you to verify that hyperbolic toral automorphisms are Anosov (i.e. the whole torus is a hyperbolic set).
• Problem 2 explores further alternative ways to characterise hyperbolic sets.
• Problem 3 is about contracting hyperbolic orbits.
• Problem 4 asks you to prove that the structure of hyperbolic sets for which $E^s$ (or $E^u$) are everywhere zero-dimensional is rather simple.