Topological Dichotomy and Strict Ergodicity for Translation Surfaces
Dynamical Systems
2007-10-02 v2 Mathematical Physics
math.MP
Abstract
In this paper the authors find examples of translation surfaces that have infinitely generated Veech groups, satisfy the topological dichotomy property that for every direction either the flow in that direction is completely periodic or minimal, and yet have minimal but non uniquely ergodic directions.
Cite
@article{arxiv.math/0607179,
title = {Topological Dichotomy and Strict Ergodicity for Translation Surfaces},
author = {Yitwah Cheung and Pascal Hubert and Howard Masur},
journal= {arXiv preprint arXiv:math/0607179},
year = {2007}
}
Comments
25 pages, 6 figures. This revision contains an improved main theorem, simplified proofs, and an application to rational billiards