How can I compute the SRB measure for the cat map? Also any pointers to references for obtaining Markov partitions and recurrence times would be lovely. Thanks

Unless I'm misinterpreting the question, the SRB measure is just Lebesgue measure... the cat map is hyperbolic, preserves area, and is topologically transitive. See Theorem 3.10 and the following remarks here: http://books.google.com/books?id=uuqeVBvQNEC&pg=PA141#v=onepage&q=&f=false 

