Cylinder deformations in orbit closures of translation surfaces
Dynamical Systems
2016-01-20 v2
Abstract
Let M be a translation surface. We show that certain deformations of M supported on the set of all cylinders in a given direction remain in the GL(2,R)-orbit closure of M. Applications are given concerning complete periodicity, field of definition, and the number of of parallel cylinders which may be found on a translation surface in a given orbit closure. The proof uses Eskin-Mirzakhani-Mohammadi's recent theorem on orbit closures of translation surfaces, as well as results of Minsky-Weiss and Smillie-Weiss on the dynamics of horocycle flow.
Cite
@article{arxiv.1302.4108,
title = {Cylinder deformations in orbit closures of translation surfaces},
author = {Alex Wright},
journal= {arXiv preprint arXiv:1302.4108},
year = {2016}
}
Comments
v2: Minor revision. Comments welcome! 24 pages