On the minimum dilatation of pseudo-Anosov homeomorphisms on surfaces of small genus

Erwan Lanneau; Jean-Luc Thiffeault

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arXiv · 0905.1302

On the minimum dilatation of pseudo-Anosov homeomorphisms on surfaces of small genus

Erwan Lanneau·Jean-Luc Thiffeault

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Abstract

We find the minimum dilatation of pseudo-Anosov homeomorphisms that stabilize an orientable foliation on surfaces of genus three, four, or five, and provide a lower bound for genus six to eight. Our technique also simplifies Cho and Ham's proof of the least dilatation of pseudo-Anosov homeomorphisms on a genus two surface. For genus g=2 to 5, the mimimum dilatation is the smallest Salem number for polynomials of degree 2g.

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Erwan Lanneau, Jean-Luc Thiffeault. 2009-05-08. On the minimum dilatation of pseudo-Anosov homeomorphisms on surfaces of small genus. https://arxiv.org/abs/0905.1302

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