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Ergodicity for infinite periodic translation surfaces

Published online by Cambridge University Press:  03 June 2013

Pascal Hubert  and
Barak Weiss
Pascal Hubert
Affiliation:
LATP, Case Cour A, Faculté des sciences de Saint Jérôme, Avenue Escadrille Normandie-Niemen, 13397 Marseille Cedex 20, France email hubert@cmi.univ-mrs.fr
Barak Weiss
Affiliation:
Ben Gurion University, Be’er Sheva, 84105, Israel email barakw@math.bgu.ac.il
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Abstract

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For a $ \mathbb{Z} $-cover $\widetilde {M} \rightarrow M$ of a translation surface, which is a lattice surface, and which admits infinite strips, we prove that almost every direction for the straightline flow is ergodic.

Keywords

ergodicityinfiniteperiodictranslation surfaces

MSC classification

Secondary: 57S25: Groups acting on specific manifolds
Type
Research Article
Information
Compositio Mathematica , Volume 149 , Issue 8 , August 2013 , pp. 1364 - 1380
Copyright
© The Author(s) 2013 

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