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

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

2010-11-02

arxiv.org/abs/1011.0700v1

Mathematics

Dynamical Systems

17 pages, 8 figures. Rewrite of portion of http://arxiv.org/abs/0802.0189

Scientific paper

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.

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