#### Volume 13, issue 4 (2009)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Editorial Procedure Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1364-0380 ISSN (print): 1465-3060 Author Index To Appear Other MSP Journals
The asymptotic behavior of least pseudo-Anosov dilatations

### Chia-Yen Tsai

Geometry & Topology 13 (2009) 2253–2278
##### Abstract

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

##### Keywords
pseudo-Anosov dilatation, minimal translation length, mapping class group, Teichmuller space
##### Mathematical Subject Classification 2000
Primary: 37E30
Secondary: 57M99, 30F60