Diophantine approximation on Veech surfaces

Details Diophantine approximation on Veech surfaces Diophantine approximation on Veech surfaces

2010-10-18

arxiv.org/abs/1010.3475v1

Mathematics

Number Theory

Scientific paper

We show that Y. Cheung's general $Z$-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.

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