Dynamics of Convex Cocompact Subgroups of Mapping Class Groups

2012/04/08 by Ilya Gekhtman, Gekhtman, Ilya
Mathematics · #Advanced Topology and Set Theory #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #math.DG #math.DS

paper · pdf · doi:10.48550/arxiv.1204.1741

Minor update, some typos corrected

arxiv created 2013/10/20 · arxiv updated 2013/10/22

Abstract

For a convex cocompact subgroup G<Mod(S), and points x,y ∈ Teich(S) we obtain asymptotic formulas as R→ ∞ of |B_R(x)∩ 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.

Related

• Uniform convergence in the mapping class group
• Dynamical properties of convex cocompact actions in projective space
• Shadows of mapping class groups: capturing convex cocompactness
• Some examples of separable convex-cocompact subgroups
• Undistorted purely pseudo-Anosov groups