I am arranging a weekly meeting of 2 hours with postgraduate students in ergodic theory (for a period of 3 weeks). I am asking here for an advice of a book (or maybe a set of papers) to look at during our reading meetings. We would like to discuss some topic of current research (say not older than 5 years), but we do not want to be too specific, because is an activity extra to our own research. At the same time, we would like to build a useful basis for further research.
For me the the classical references are:
- An Introduction to Ergodic Theory (Graduate Texts in Mathematics) by Peter Walters.
- Ergodic Theory (Cambridge Studies in Advanced Mathematics) by Karl E. Petersen.
- Introduction to the Modern Theory of Dynamical Systems (Encyclopedia of Mathematics and its Applications) by Anatole Katok and Boris Hasselblatt.
- Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms (Lecture Notes in Mathematics) by Robert Edward Bowen, Jean-René Chazottes and David Ruelle.
- Ergodic Theory: With a View Towards Number Theory (Graduate Texts in Mathematics) by Thomas Ward, Manfred Einsiedler.