# Problem Sheet R

This Problem Sheet is based on Lectures 38 and 39.

- Problem 1 asks you to prove that the difference between a norm and its box adjustment can be controlled by angle between the two subspaces.
- Problems 2 and 3 are about
*dominated splittings*. This gives rise to the notion of*partial hyperbolicity*(see the footnote to Problem 2). - Problem 4 shows that hyperbolic sets on manifolds can be reduced to linear hyperbolic systems, at the expense of moving into infinite dimensions. This problem is quite hard. ðŸ˜ˆ

Comments and questions?