Generalized staircases: Recurrence and symmetry

W. Patrick Hooper, Barak Weiss

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


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 Schmithüsen, we provide examples of infinite non-arithmetic lattice surfaces, as well as surfaces with infinitely generated Veech groups.

Original languageEnglish
Pages (from-to)1581-1600
Number of pages20
JournalAnnales de l'Institut Fourier
Issue number4
StatePublished - 12 Oct 2012


  • Infinite translation surfaces
  • Lattices
  • Straightline flow
  • Veech groups

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology


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