Pseudo-Anosov homeomorphisms on translation surfaces in hyperelliptic components have large entropy - Ecole Centrale de Marseille Accéder directement au contenu
Article Dans Une Revue Geometric And Functional Analysis Année : 2012

Pseudo-Anosov homeomorphisms on translation surfaces in hyperelliptic components have large entropy

Résumé

We prove that the dilatation of any pseudo-Anosov homeomorphism on a translation surface that belong to a hyperelliptic component is bounded from below uniformly by sqrt{2}. This is in contrast to Penner's asymptotic. Penner proved that the logarithm of the least dilatation of any pseudo-Anosov homeomorphism on a surface of genus g tends to zero at rate 1/g (as g goes to infinity). We also show that our uniform lower bound sqrt{2} is sharp. More precisely the least dilatation of a pseudo-Anosov on a genus g>1 translation surface in a hyperelliptic component belongs to the interval ]sqrt{2},sqrt{2}+2^{1-g}[. The proof uses the Rauzy-Veech induction.

Dates et versions

hal-01230597 , version 1 (18-11-2015)

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Citer

Corentin Boissy, Erwan Lanneau. Pseudo-Anosov homeomorphisms on translation surfaces in hyperelliptic components have large entropy. Geometric And Functional Analysis, 2012, 22 (01), pp.74-106. ⟨10.1007/s00039-012-0152-0⟩. ⟨hal-01230597⟩
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