Problem Sheet R
- 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. 😈
Comments and questions?