Generalized staircases: recurrence and symmetry

Abstract

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.

13 pages, 3 figures

Cited by in corpus (6)

• Non-ergodic Z-periodic billiards and infinite translation surfaces
• Ergodic directions for billiards in a strip with periodically located obstacles
• Geometry, topology and dynamics of geodesic flows on noncompact polygonal surfaces
• Recurrence in generic staircases
• A series of coverings of the regular n-gon
• Ergodic properties of infinite extensions of area-preserving flows