2006/07/17 by Ursula Hamenstaedt, Hamenstaedt, Ursula
Mathematics · Physics and Astronomy · #30F60 #37A20 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Quantum chaos and dynamical systems
paper · pdf · doi:10.48550/arxiv.math/0607386
openalex publication_date 2006/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.