Diophantine approximation on Veech surfaces
Number Theory
2010-10-19 v1 Dynamical Systems
Abstract
We show that Y. Cheung's general -continued fractions can be adapted to give approximation by saddle connection vectors for any compact translation surface. That is, we show the finiteness of his Minkowski constant for any compact translation surface. Furthermore, we show that for a Veech surface in standard form, each component of any saddle connection vector dominates its conjugates. The saddle connection continued fractions then allow one to recognize certain transcendental directions by their developments.
Keywords
Cite
@article{arxiv.1010.3475,
title = {Diophantine approximation on Veech surfaces},
author = {Pascal Hubert and Thomas A. Schmidt},
journal= {arXiv preprint arXiv:1010.3475},
year = {2010}
}