arXiv Analytics

Sign in

arXiv:0802.0189 [math.DS]AbstractReferencesReviewsResources

Dynamics on an infinite surface with the lattice property

W. Patrick Hooper

Published 2008-02-01Version 1

Dynamical systems on an infinite translation surface with the lattice property are studied. The geodesic flow on this surface is found to be recurrent in all but countably many rational directions. Hyperbolic elements of the affine automorphism group are found to be nonrecurrent, and a precise formula regarding their action on cylinders is proven. A deformation of the surface in the space of translation surfaces is found, which "behaves nicely" with the geodesic flow and action of the affine automorphism group.

Comments: 48 pages, 11 figures
Categories: math.DS
Subjects: 37D40, 37D50, 37E99, 32G15
Related articles: Most relevant | Search more
arXiv:0801.3951 [math.DS] (Published 2008-01-25)
Symbolic dynamics for the geodesic flow on Hecke surfaces
arXiv:1008.0367 [math.DS] (Published 2010-08-02, updated 2013-05-13)
Symbolic Dynamics for the Geodesic Flow on Two-dimensional Hyperbolic Good Orbifolds
arXiv:2205.14848 [math.DS] (Published 2022-05-30)
Homoclinics for geodesic flows of surfaces

Links

Toolbox