Pseudo-Anosov Homeomorphisms on Translation Surfaces in Hyperelliptic Components Have Large Entropy

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作者
Corentin Boissy
Erwan Lanneau
机构
[1] Université Paul Cézanne,Laboratoire d’Analyse, Topologie et Probabilité
[2] Faculté de Saint Jérôme,undefined
[3] Centre de Physique Théorique (CPT),undefined
[4] UMR CNRS 6207 Université du Sud Toulon-Var and Fédération de Recherches des Unités de Mathématiques de Marseille Luminy,undefined
来源
Geometric and Functional Analysis | 2012年 / 22卷
关键词
Pseudo-Anosov homeomorphisms; Interval exchange transformations; Rauzy–Veech induction; Moduli spaces; Primary: 37D40; Secondary: 37E05;
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摘要
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} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \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).
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页码:74 / 106
页数:32
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