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Genus-one Birkhoff sections for geodesic flows

Published online by Cambridge University Press:  11 August 2014

PIERRE DEHORNOY
PIERRE DEHORNOY*
Affiliation:
Mathematisches Institut, Universität Bern, Sidlerstrasse 5, 3012 Bern, Switzerland email [email protected] Present address: Institut Fourier, Université Joseph Fourier-Grenoble 1, 100 rue des mathématiques, BP74, 38402 Saint-Martin-d’H\`eres cedex, France
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Abstract

We prove that the geodesic flow on the unit tangent bundle to every hyperbolic 2-orbifold that is a sphere with three or four singular points admits explicit genus-one Birkhoff sections, and we determine the associated first return maps.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 35 , Issue 6 , September 2015 , pp. 1795 - 1813
Copyright
© Cambridge University Press, 2014 

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