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Spring 2008 (Monday, January 21 to Friday, March 14; Monday, April 28 to Friday, May 16)
No prerequisites information is available yet.
- Lecture 1: Examples of dynamical systems (maps on a circle, the doubling map, shifts of finite type, toral automorphisms, the geodesic flow)
- Lecture 2: Uniform distribution, inc. applications to number theory
- Lecture 3: Invariant measures and measure-preserving transformations. Ergodicity.
- Lecture 4: Recurrence and ergodic theorems (Poincaré recurrence, Kac's lemma, von Neumann's ergodic theorem, Birkhoff's ergodic theorem)
- Lecture 5: Applications of the ergodic theorem (normality of numbers, the Hopf argument, etc)
- Lecture 6: Mixing. Spectral properties.
- Lecture 7: Entropy and the isomorphism problem.
- Lecture 8: Topological pressure and the variational principle.
- Lecture 9: Thermodynamic formalism and transfer operators.
- Lecture 10: Applications of thermodynamic formalism: (i) Bowen's formula for Hausdorff dimension, (ii) central limit theorems.
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