Mathematics – Dynamical Systems
Scientific paper
2011-12-28
Mathematics
Dynamical Systems
78 p, 4 figures
Scientific paper
Let S be an oriented surface of genus g with m punctures and 3g-3+m>1. For each component of a stratum in the moduli space of quadratic or abelian differentials, we construct a subshift of finite type and a Borel suspension which admits a finite-to-one semi-conjugacy into the Teichmueller flow on Q. This is used to show that the Lebesgue measure on Q is the unique measure of maximal entropy. If h is the entropy of the Lebesgue measure, then for every a>0 there is a compact subset K of Q such that the entropy of an invariant Borel probability measure on Q-K does not exceed h-1+a. Moreover, the growth rate of periodic orbits in Q-K does not exceed h-1+a$. This implies that the number of periodic orbits in Q of period at most R is asymptotic to exp(hR)/hR.Finally we give a unified and simplified proof of exponential mixing for the Lebesgue measure on strata.
Hamenstaedt Ursula
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