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. 😈

Comments and questions?