I had the pleasure of being invited to give a minicourse in the Wandering Seminar.
I have given five 90 minutes lectures on the almost Borel structure of diffeomorphisms with some hyperbolicity. This is a joint work with Mike Boyle and relying on Sarig’s Markov extensions.
- lecture 1 (categories of dynamical systems, basics of entropy, exercises)
- lecture 2 (Lyapunov exponents, Oseledets theorem, applications)
- lecture 3 (Ruelle’s inequality, uniform hyperbolicity, shadowing)
- lecture 4 (Pesin theory, Katok’s horseshoe theorem, Markov shifts)
- lecture 5 (Hochman universality result, universal parts, characterization of Markov shifts, conclusion)
The last slides includes references