most recent 30 from http://mathoverflow.net 2013-05-22T04:54:14Z http://mathoverflow.net/feeds/question/36070 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/36070/exactness-of-the-gauss-transformation Steven Neutral 2010-08-19T10:07:00Z 2010-09-01T18:17:29Z

<p>Dear all,</p> <p>I would like to know if the Gauss transformation <em>T(x) = fractional part of 1/x, x in (0,1)</em> (with the Gauss invariant probability measure) is an exact endomorphism (in the sense of Rokhlin). I have failed to find an answer in the literature, any reference would be welcomed. </p>

http://mathoverflow.net/questions/36070/exactness-of-the-gauss-transformation/36073#36073 Matheus 2010-08-19T11:00:20Z 2010-08-19T11:00:20Z

<p>Hi Steven,</p> <p>the answer to your question is yes and there are several ways of deriving the exactness of Gauss map with respect to Gauss probability: for instance, in this <a href="http://w3.impa.br/~viana/out/sdds.pdf" rel="nofollow">text</a> of M. Viana, it is derived as a consequence of the proof of the exponential decay of correlations.</p>