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Pseudo-Anosov Homeomorphisms on Translation Surfaces in Hyperelliptic Components Have Large Entropy |
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| Authors: | Corentin Boissy Erwan Lanneau |
| Institution: | 1. Laboratoire d??Analyse, Topologie et Probabilit??, Universit?? Paul C??zanne, Facult?? de Saint J??r?me, Avenue Escadrille Normandie-Niemen, case cour A, 13397, Marseille cedex 20, France 2. Centre de Physique Th??orique (CPT), UMR CNRS 6207 Universit?? du Sud Toulon-Var and F??d??ration de Recherches des Unit??s de Math??matiques de Marseille Luminy, Case 907, F-13288, Marseille Cedex 9, France |
| Abstract: | 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 ?2{\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). |
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