There are no announcements
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.
No bibliography has been specified for this course.
No assessment information is available yet.
No assignments have been set for this course.
Files marked L are intended to be displayed on the main screen