The asymptotic behavior of least pseudo-Anosov dilatations

By Chia-yen Tsai. 2008

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For a surface $S$ with $n$ marked points and fixed genus $g\geq2$, 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 $1/n$.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/59cdc13d770d086da07e1a4b5aee3289709c2cf9