# 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

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topHooper, 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 -

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