English

An Infinite Surface With The Lattice Property I: Veech Groups and Coding Geodesics

Dynamical Systems 2012-09-04 v2

Abstract

We study the symmetries and geodesics of an infinite translation surface which arises as a limit of translation surfaces built from regular polygons, studied by Veech. We find the affine symmetry group of this infinite translation surface, and we show that this surface admits a deformation into other surfaces with topologically equivalent affine symmetries. The geodesics on these new surfaces are combinatorially the same as the geodesics on the original.

Keywords

Cite

@article{arxiv.1011.0700,
  title  = {An Infinite Surface With The Lattice Property I: Veech Groups and Coding Geodesics},
  author = {W. Patrick Hooper},
  journal= {arXiv preprint arXiv:1011.0700},
  year   = {2012}
}

Comments

23 pages, 10 figures. Improved exposition. Theorem 10 is an improved geodesic coding result. arXiv admin note: text overlap with arXiv:0802.0189

R2 v1 2026-06-21T16:37:57.457Z