Generalized Staircases: Recurrence and Symmetry

By Barak Weiss. 2009

62 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/6d8c0c1ce15b10647f12baeb922b61db7b8ed5a5

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

1. C. Ulcigrai
2. Krzysztof Frkaczek
3. Corentin Boissy

In Mathematical Physics

1. C. Ulcigrai
2. Krzysztof Frkaczek
3. Corentin Boissy

Citations in the corpus

• CONNECTED COMPONENTS OF THE STRATA OF THE MODULI SPACE OF MEROMORPHIC DIFFERENTIALS (2012, background): “For instance, dynamics on Z covers of compact translation surfaces (see [8, 10, 5]), infinite square tiled surfaces (see [11]), or general noncompact surfaces (see [2, 3, 19]).”
• Non-ergodic Z-periodic billiards and infinite translation surfaces (2011, background): “5 (see [29]) The Z-cover ( ̃ Mγ , ω̃γ ) of the translation surface (M,ω) given by γ ∈H1(M,Z) is called recurrent if hol(γ )= 0.”