论文信息 - Growth of pseudo-Anosov conjugacy classes in Teichmüller space

Growth of pseudo-Anosov conjugacy classes in Teichmüller space

Athreya, Bufetov, Eskin and Mirzakhani [2] have shown the number of mapping class group lattice points intersecting a closed ball of radius R in Teichmüller space is asymptotic to e, where h is the dimension of the Teichmüller space. We show for any pseudo-Anosov mapping class f , there exists a power n, such that the number of lattice points of the f conjugacy class intersecting a closed ball of radius R is coarsely asymptotic to e h 2 .

Jiawei Han | Jiawei Han

[1] Lattice Point Asymptotics and Volume Growth on Teichmuller space. , 2006, math/0610715.

[2] Joseph Maher. Asymptotics for Pseudo-Anosov Elements in Teichmüller Lattices , 2009, 0901.2679.

[3] G. Arzhantseva,et al. Growth tight actions , 2014, 1401.0499.

[4] Y. Minsky. Quasi-projections in Teichmüller space. , 1994 .

[5] D. Mumford. A remark on Mahler’s compactness theorem , 1971 .

[6] Steven P. Kerckho,et al. The Nielsen realization problem , 1983 .

[7] R. Phillips,et al. The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces , 1982 .

[8] D. Dumas. Skinning maps are finite-to-one , 2012, 1203.0273.

[9] Jouni Parkkonen,et al. On the hyperbolic orbital counting problem in conjugacy classes , 2013, 1312.1893.

[10] W. Thurston. On the geometry and dynamics of diffeomorphisms of surfaces , 1988 .