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

Erwan Lanneau; Jean-Luc Thiffeault — 2011

Annales de l’institut Fourier

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 minimum dilatation is the smallest Salem number for polynomials of degree $2 g$ .

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