arXiv 0905.37362009-05-22math.DS

Generalized staircases: recurrence and symmetry

W. Patrick Hooper, Barak Weiss

备注：: 13 pages, 3 figures

英文摘要：

We study infinite translation surfaces which are Z-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 Schmithusen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

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