Recommended Background
Only basic knowledge will be assumed in ergodic theory, as it can be
found for instance in the beginning of Walter's book, including the
concepts of invariant measures, ergodicity, the mean and pointwise
ergodic theorems, Poincaré recurrence theorem, and the definitions of
entropy. Some chapters of a forthcoming book by Einsiedler and
Ward are already available and form a valuable introduction.
Basics of Fourier analysis on compact abelian groups, modest commutative
algebra and number theory, including p-adic numbers, uniform distribution,
introductory diophantine approximation will be also expected.
The course of M. Einsiedler will assume only minimal knowledge about Lie
groups, for instance Chapter 0 of Knapp's book.
Recommended Reading
- Yann Bugeaud, Approximation by Algebraic Numbers,
Cambridge Tracts in Mathematics 160, Cambridge University Press, 2004.
- Anton Deitmar, A first Course in Harmonic Analysis, Universitext, Springer,
2000
- Manfred Einsiedler and Thomas Ward,
Ergodic Theory: with a View
Towards Number Theory".
- Graham Everest and Thomas Ward, Heights of Polynomials and Entropy in
Algebraic Dynamics, Springer 1999
- Hillel Furstenberg,
Recurrence in Ergodic Theory and Combinatorial Number Theory,
Princeton University Press 1981
- Hardy and Wright, An Introduction to the Theory of Numbers,
Oxford University Press, 1979
- Anthony Knapp, Lie Groups beyond an Introduction,
Progress in Mathematics 140, Birkhäuser, 2002
- Serge Lang, Algebra, Graduate Texts in Mathematics 211, Springer, 2002
- Douglas Lind and Brian Marcus,
An Introduction to Symbolic Dynamics and Coding,
Cambridge University Press 1995
- Walter Rudin, Fourier Analysis on Groups, Wiley Classics Library, 1962
- Peter Walters, An Introduction to Ergodic Theory, Springer 1982