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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:

The classical theorem of Poincaré on recurrence only gives information of qualitative nature. On the other hand it is clearly a matter of intrinsic difficulty and not of lack of interest that less is known concerning the quantitative behavior of recurrence. Here we discuss recent developments that include the almost everywhere coincidence between the recurrence rate and the pointwise dimension in the case of hyperbolic dynamics. We also discuss the almost product structure of recurrence, which closely imitates the product structure provided by the families of stable and unstable manifolds as well as the almost product structure of hyperbolic measures.
show/hide this revision's text 1

I like this 2006 paper by Luis Barreira (cited in the Wikipedia article), which I encountered when pursuing this MO question on billiard trajectories: "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:

The classical theorem of Poincaré on recurrence only gives information of qualitative nature. On the other hand it is clearly a matter of intrinsic difficulty and not of lack of interest that less is known concerning the quantitative behavior of recurrence. Here we discuss recent developments that include the almost everywhere coincidence between the recurrence rate and the pointwise dimension in the case of hyperbolic dynamics. We also discuss the almost product structure of recurrence, which closely imitates the product structure provided by the families of stable and unstable manifolds as well as the almost product structure of hyperbolic measures.