# Problem Sheet I

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 $S^1$.

Comments and questions?