Generalized Staircases: Recurrence and Symmetry

W. Patrick Hooper[1]; Barak Weiss[2]

  • [1] The City College of New York New York, NY, USA 10031
  • [2] Ben Gurion University, Be’er Sheva, Israel 84105

Annales de l’institut Fourier (2012)

  • Volume: 62, Issue: 4, page 1581-1600
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Hooper, W. Patrick, and Weiss, Barak. "Generalized Staircases: Recurrence and Symmetry." Annales de l’institut Fourier 62.4 (2012): 1581-1600. <http://eudml.org/doc/251026>.

@article{Hooper2012,
abstract = {We study infinite translation surfaces which are $\mathbb\{Z\}$-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.},
affiliation = {The City College of New York New York, NY, USA 10031; Ben Gurion University, Be’er Sheva, Israel 84105},
author = {Hooper, W. Patrick, Weiss, Barak},
journal = {Annales de l’institut Fourier},
keywords = {Infinite translation surfaces; Veech groups; lattices; straightline flow; infinite translation surfaces},
language = {eng},
number = {4},
pages = {1581-1600},
publisher = {Association des Annales de l’institut Fourier},
title = {Generalized Staircases: Recurrence and Symmetry},
url = {http://eudml.org/doc/251026},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Hooper, W. Patrick
AU - Weiss, Barak
TI - Generalized Staircases: Recurrence and Symmetry
JO - Annales de l’institut Fourier
PY - 2012
PB - Association des Annales de l’institut Fourier
VL - 62
IS - 4
SP - 1581
EP - 1600
AB - We study infinite translation surfaces which are $\mathbb{Z}$-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.
LA - eng
KW - Infinite translation surfaces; Veech groups; lattices; straightline flow; infinite translation surfaces
UR - http://eudml.org/doc/251026
ER -

References

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