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Dear all,

I would like to know if the Gauss transformation T(x) = fractional part of 1/x, x in (0,1) (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.

edited Sep 1 2010 at 18:17

Ian Morris
1,951●8●17

asked Aug 19 2010 at 10:07

Steven Neutral
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Matheus · Accepted Answer · 2010-08-19 11:00:20Z UTC

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Hi Steven,

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 text of M. Viana, it is derived as a consequence of the proof of the exponential decay of correlations.

answered Aug 19 2010 at 11:00

Matheus
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Thank you. I would also like to learn about the others ways to derive this result. For instance, does there exist more elementary ways ? – Steven Neutral Aug 19 2010 at 13:09

exactness of the Gauss transformation

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