Bowen's construction for the Teichmüller flow
Ursula Hamenstädt
Journal of Modern Dynamics 2013, 7(4): 489-526 doi: 10.3934/jmd.2013.7.489
Let ${\cal Q}$ be a connected component of a stratum in the moduli space of abelian or quadratic differentials for a nonexceptional Riemann surface $S$ of finite type. We prove that the probability measure on ${\cal Q}$ in the Lebesgue measure class which is invariant under the Teichmüller flow is obtained by Bowen's construction.
keywords: Strata Teichmüller flow equidistribution. periodic orbits
Dynamics of the Teichmüller flow on compact invariant sets
Ursula Hamenstädt
Journal of Modern Dynamics 2010, 4(2): 393-418 doi: 10.3934/jmd.2010.4.393
Let $S$ be an oriented surface of genus $g\geq 0$ with $m\geq 0$ punctures and $3g-3+m\geq 2$. For a compact subset $K$ of the moduli space of area-one holomorphic quadratic differentials for $S$, let $\delta(K)$ be the asymptotic growth rate of the number of periodic orbits for the Teichmüller flow $\Phi^t$ which are contained in $K$. We relate $\delta(K)$ to the topological entropy of the restriction of $\Phi^t$ to $K$. Moreover, we show that sup$_K\delta(K)=6g-6+2m$.
keywords: orbit counting Teichmüller flow Anosov closing expansive entropy

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