This Problem Sheet is based on Lectures 17 and 18.

• Problem 1 gives an example of a continuous function that does not have bounded variation.
• Problem 2 shows that the rotation number of the composition of two commuting systems is their sum.
• Problem 3 shows that the analogue of the Poincaré Classification Theorem does not hold when the rotation number is rational.
• Problem 4 is about the non-wandering set of an orientation-preserving reversible dynamical system on $S^1$ with irrational rotation number.
• Problem 5 is about the chain recurrent set of an an orientation-preserving reversible dynamical system on $S^1$.