Problem Sheet T
- Problems 1 and 2 ask you prove Lemma 47.2 and Remark 47.3, which I skipped in class.
- Problems 3 and 4 are about Anosov diffeomorphisms whose non-wandering set is the entire manifold.
Remark: It is an open conjecture that the non-wandering set of an Anosov diffeomorphism is always the entire manifold. This has been proved in many situations (for example, for Anosov diffeomorphisms on (infra)nilmanifolds), but remains open in general. However it is false for Anosov flows.
- Problem 5 asks you to show that Axiom A is a generalisation of the Anosov condition.
This is the last problem sheet of the year! 😀
Comments and questions?