Dynamics of Convex Cocompact Subgroups of Mapping Class Groups

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 $PMF$.

Minor update, some typos corrected

References in corpus (3)

• Convex cocompact subgroups of mapping class groups
• Lattice Point Asymptotics and Volume Growth on Teichmuller space
• Counting closed geodesics on rank one manifolds

Cited by in corpus (1)

• Counting conjugacy classes of fully irreducibles: double exponential growth