Pseudo-Anosov maps with small stretch factors on punctured surfaces

Mehdi Yazdi

doi:10.2140/agt.2020.20.2095

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arXiv · 1801.01754

Pseudo-Anosov maps with small stretch factors on punctured surfaces

Mehdi Yazdi

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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 behaviour of this minimum number for a certain large subset of the $(g,n)$ plane, up to a multiplicative constant. In particular it has been shown that for fixed $n$, this minimum value behaves as $\frac{1}{g}$, proving what Penner speculated in 1991.

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Mehdi Yazdi. 2018-01-05. Pseudo-Anosov maps with small stretch factors on punctured surfaces. https://doi.org/10.2140/agt.2020.20.2095

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