MA 346: Ergodic theory
Credits: 3:0
Prerequisites :
- Measure theory
- Elements of Functional analysis.
- It would help to have some familiarity with Fourier analysis and some probability theory.
Measure preserving systems, Poincare recurrence, von Neumann ergodic theorem,
Khintichine’s theorem, spectral theorem and applications to combinatorics, ergodicity, Birkhoff
ergodic theorem, mixing, unique ergodicity, disintegration of measures, Furstenberg
correspondence principle, Furstenberg-Sarkozy theorem, Jacobs-de Leevuw-Glicksberg
decomposition theorem and application to Roth’s theorem, The Kronecker Factor. (Additional
material: Bhattcharya’s proof of the periodic tiling conjecture in $\Z$^2)
Suggested books and references:
- Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag (1982).
- Manfred Einsiedler and Thomas Ward, Ergodic Theory with a view Towards Number Theory, Springer-Verlag (2012).
- Karl E. Petersen, Ergodic Theory, Cambridge university press (1983).