1. Dynamical systems with an invariant
measure. Poincaré’s recurrence. The Bogoliubov-Krylov theorem.
2. The ergodic theorems of von
Neumann and Birkhoff. Weyl’s ergodic theorem.
3. Mixing and ergodicity.
4. Metric entropy. Topological
entropy. The variational principle.
5. Special classes of mappings. Piecewise
monotonic mappings. Denjoy diffeomorphisms. Billiards.
6. Recurrence and its applications to
combinatorics. The theorems of van der Waerden and Szemeredi.
7. The ergodic theorem of Oseledec. Liapunov
Exponents. Applications to chaotic dynamical systems.
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