Hello everybody! Recently I start a reading of a survey by Benoit Saussol, AN INTRODUCTION TO QUANTITATIVE POINCARE RECURRENCE IN DYNAMICAL SYSTEMS, I am interested in references (Papers) Basics Poincare Recurrence. I know that this survey is already basic, but wanted to know more references of this kind and I would also references to where I can find open problems in this matter. I would also references to applications of this theory in other fields in mathematics.
Joseph's answer is the first place I would (and did) look for information on this topic. However there are a couple of recent ancillary references along these lines that may be helpful. For instance, see
M. S. Baptista et al., "Kolmogorov–Sinai entropy from recurrence times". Phys. Lett. A 374, 1135 (2010)
the obvious cite
L. Barreira and B. Saussol, "Product structure of Poincar\'e recurrence". Ergodic Th. Dyn. Sys. 22, 33 (2002)
G. Robinson and M. Thiel, "Recurrences determine the dynamics". Chaos 19, 023104 (2009).
I like this 2006 paper by Luis Barreira (cited in the Wikipedia article), which I encountered when pursuing this MO question on billiard trajectories (which you might visit): "Poincaré recurrence: Old and new" (in Zambrini, Jean-Claude, XIVth International Congress on Mathematical Physics, World Scientific, pp. 415–422.) You can get a preliminary version from citeseer here. Here is the Abstract: