Generalized staircases: recurrence and symmetry

Details Generalized staircases: recurrence and symmetry Generalized staircases: recurrence and symmetry

2009-05-22

arxiv.org/abs/0905.3736v1

Mathematics

Dynamical Systems

13 pages, 3 figures

Scientific paper

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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