Bernoulli measures for the Teichmueller flow

Details Bernoulli measures for the Teichmueller flow Bernoulli measures for the Teichmueller flow

2006-07-17

arxiv.org/abs/math/0607386v4

Mathematics

Dynamical Systems

The paper is superceded by math/0703602, by 0705.3812 and by "Symbolic dynamics of the Teichmueller flow"

Scientific paper

Let S be a nonexceptional oriented surface of finite type. We construct an uncountable family of probability measures on the space of area on holomorphic quadratic differentials over the moduli space for S containing the usual Lebesgue measure. These measures are invariant under the Teichmueller geodesic flow, and they are mixing, absolutely continuous with respect to the stable and unstable foliation adn exponentially recurrent to a compact set. Finally we show that the critical exponent of the mapping class group equals the dimension of the Teichmueller space for S. Moreover, this critical exponent coincides with the the logarithmic asymptotic of the number of closed Teichmueller geodesics in moduli space which meet a sufficiently large compact set.

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