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arXiv · 2105.08640

Growth of Pseudo-Anosov Conjugacy Classes in Teichm\"{u}ller Space

Jiawei Han
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Abstract

Athreya, Bufetov, Eskin and Mirzakhani have shown the number of mapping class group lattice points intersecting a closed ball of radius $R$ in Teichm\"{u}ller space is asymptotic to $e^{hR}$, where $h$ is the dimension of the Teichm\"{u}ller 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 $e^{\frac{h}{2}R}$.

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Jiawei Han. 2021-05-18. Growth of Pseudo-Anosov Conjugacy Classes in Teichm\"{u}ller Space. https://arxiv.org/abs/2105.08640

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