We prove that the dilatation of any pseudo-Anosov homeomorphism on a translation surface that belongs to a hyperelliptic component is bounded from below uniformly by \documentclass[12pt]{minimal}
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\begin{document}$${\sqrt{2}}$$\end{document} . 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).
机构:
Univ Paul Cezanne, Lab Anal Topol & Probabilite, Fac St Jerome, F-13397 Marseille 20, FranceUniv Paul Cezanne, Lab Anal Topol & Probabilite, Fac St Jerome, F-13397 Marseille 20, France
Boissy, Corentin
Lanneau, Erwan
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机构:
Univ Sud Toulon Var, CPT, UMR CNRS 6207, F-13288 Marseille 9, France
Federat Rech Unites Math Marseille Luminy, Case 907, F-13288 Marseille 9, FranceUniv Paul Cezanne, Lab Anal Topol & Probabilite, Fac St Jerome, F-13397 Marseille 20, France