Dynamics of Convex Cocompact Subgroups of Mapping Class Groups

Details Dynamics of Convex Cocompact Subgroups of Mapping Class Groups Dynamics of Convex Cocompact Subgroups of Mapping Class Groups

2012-04-08

arxiv.org/abs/1204.1741v1

Mathematics

Dynamical Systems

Scientific paper

For a convex cocompact subgroup $Gobtain 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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