Generalized Staircases: Recurrence and Symmetry
Annales de l'Institut Fourier, Volume 62 (2012) no. 4, pp. 1581-1600.

We study infinite translation surfaces which are -covers of compact translation surfaces. We obtain conditions ensuring that such surfaces have Veech groups which are Fuchsian of the first kind and give a necessary and sufficient condition for recurrence of their straight-line flows. Extending results of Hubert and Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

Nous étudions les -revêtements de translation des surfaces de translation compactes. Nous donnons des conditions nécessaires pour que le groupe de Veech soit fuchsien du premier type, et une condition nécessaire et suffisante pour la récurrence du flot directionnel. En étendant des résultats de Hubert et Schmithüsen, nous donnons des exemples non-arithmétiques dont le groupe de Veech est un réseau et des exemples à groupe de Veech de type infini.

DOI: 10.5802/aif.2730
Classification: 11Y40, 12Y05, 37M99, 52C99
Keywords: Infinite translation surfaces, Veech groups, lattices, straightline flow
Mot clés : Surfaces de translation infini, Groupes de Veech, Reseau, Flot directionnel
Hooper, W. Patrick 1; Weiss, Barak 2

1 The City College of New York New York, NY, USA 10031
2 Ben Gurion University, Be’er Sheva, Israel 84105
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Hooper, W. Patrick; Weiss, Barak. Generalized Staircases: Recurrence and Symmetry. Annales de l'Institut Fourier, Volume 62 (2012) no. 4, pp. 1581-1600. doi : 10.5802/aif.2730. http://www.numdam.org/articles/10.5802/aif.2730/

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