Growth of pseudo-Anosov conjugacy classes in Teichmüller space (Q6062655)

Summary: \textit{J. Athreya} et al. [Duke Math. J. 161, No. 6, 1055--1111 (2012; Zbl 1246.37009)] have shown that the number of mapping class group lattice points intersecting a closed ball of radius \(R\) in Teichmüller space is asymptotic to \(e^{hR}\), 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 \(f^n\) conjugacy class intersecting a closed ball of radius \(R\) is coarsely asymptotic to \(e^{\frac{h}{2}R}\).