MA 346: Ergodic theory

Credits: 3:0

Pre-requisites :

1. Measure theory
2. Elements of Functional analysis.
3. 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:

1. Peter Walters, An Introduction to Ergodic Theory, Springer-Verlag (1982).
2. Manfred Einsiedler and Thomas Ward, Ergodic Theory with a view Towards Number Theory, Springer-Verlag (2012).
3. Karl E. Petersen, Ergodic Theory, Cambridge university press (1983).

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