The Arnold cat map - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-24T20:06:12Z http://mathoverflow.net/feeds/question/4001 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/4001/the-arnold-cat-map The Arnold cat map Steve Huntsman 2009-11-03T21:23:38Z 2010-02-16T15:01:59Z <p>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</p> http://mathoverflow.net/questions/4001/the-arnold-cat-map/4004#4004 Answer by Martin M. W. for The Arnold cat map Martin M. W. 2009-11-03T22:05:29Z 2009-11-03T22:05:29Z <p>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: <a href="http://books.google.com/books?id=uu-qeVBvQNEC&amp;pg=PA141#v=onepage&amp;q=&amp;f=false" rel="nofollow">http://books.google.com/books?id=uu-qeVBvQNEC&amp;pg=PA141#v=onepage&amp;q=&amp;f=false</a></p>