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arXiv · 1204.1741

Dynamics of Convex Cocompact Subgroups of Mapping Class Groups

Ilya Gekhtman
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Abstract

For a convex cocompact subgroup $G<Mod(S)$, and points $x,y \in Teich(S)$ we obtain asymptotic formulas as $R\to \infty$ of $|B_{R}(x)\cap Gy|$ as well as the number of conjugacy classes of pseudo-Anosov elements in $G$ of dilatation at most $R$. We do this by developing an analogue of Patterson-Sullivan theory for the action of $G$ on $PMF$.

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Ilya Gekhtman. 2012-04-08. Dynamics of Convex Cocompact Subgroups of Mapping Class Groups. https://arxiv.org/abs/1204.1741

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