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.


Many thanks.



Ergodic theory and dynamical systems books references
For a beautiful overview, focusing on entropy and the variational principle, you can't beat Walters' book. I've given reading courses from it, and it is very well written and excellent for self-study. 


The Einsiedler-Ward book (the first of a projected three volumes, parts of the second and third books are viewable at <http://maths.dur.ac.uk/~tpcc68/welcome.html>) also covers the basics extremely well and at a leisurely pace, with more emphasis on topics crucial to deep applications of dynamics to number theory via homogeneous spaces, which is a very active research area.


Given your short time frame, I'd suggest using Walters as the basic text, but also browsing Einsiedler-Ward for topics of more current research interest. Should any students get interested enough to delve more deeply, then a more systemic reading of Einsiedler-Ward would provide them with a very solid foundation.


