#### Volume 20, issue 4 (2020)

 Recent Issues
 The Journal About the Journal Editorial Board Editorial Interests Subscriptions Submission Guidelines Submission Page Policies for Authors Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 Author Index To Appear Other MSP Journals
Pseudo-Anosov maps with small stretch factors on punctured surfaces

### Mehdi Yazdi

Algebraic & Geometric Topology 20 (2020) 2095–2128
##### Abstract

Consider the problem of estimating the minimum entropy of pseudo-Anosov maps on a surface of genus $g$ with $n$ punctures. We determine the behavior of this minimum number for a certain large subset of the $\left(g,n\right)$ plane, up to a multiplicative constant. In particular, we show that for fixed $n$, this minimum value behaves as $\frac{1}{g}$, proving what Penner speculated in 1991.

##### Keywords
pseudo-Anosov, entropy, stretch factor, dilatation, punctured surfaces
##### Mathematical Subject Classification 2010
Primary: 37B40, 37E30