## Ergodic Theory (MAGIC010) |

## General## SemesterSpring 2008 (Monday, January 21 to Friday, March 14; Monday, April 28 to Friday, May 16) ## Timetable- Wed 12:05 - 12:55
## PrerequisitesNo prerequisites information is available yet.
## Syllabus-
**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.
## Students
## BibliographyNo bibliography has been specified for this course. ## AssessmentNo assessment information is available yet.
No assignments have been set for this course. ## FilesFiles marked |