The asymptotic behavior of least pseudo-Anosov dilatations

Chia-Yen Tsai

doi:10.2140/gt.2009.13.2253

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Home > Journals > Geom. Topol. > Volume 13 > Issue 4 > Article

2009 The asymptotic behavior of least pseudo-Anosov dilatations

Chia-Yen Tsai

Geom. Topol. 13(4): 2253-2278 (2009). DOI: 10.2140/gt.2009.13.2253

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Abstract

For a surface $S$ with $n$ marked points and fixed genus $g \geq 2$ , we prove that the logarithm of the minimal dilatation of a pseudo-Anosov homeomorphism of $S$ is on the order of $log (n) ∕ n$ . This is in contrast with the cases of genus zero or one where the order is $1 ∕ n$ .

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Chia-Yen Tsai. "The asymptotic behavior of least pseudo-Anosov dilatations." Geom. Topol. 13 (4) 2253 - 2278, 2009. https://doi.org/10.2140/gt.2009.13.2253