Diophantine approximation on Veech surfaces

2010/10/18 by Pascal Hubert, Thomas Schmidt, Hubert, Pascal +1
Chemistry · Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Chromatography in Natural Products #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1010.3475

openalex publication_date 2010/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Geodesic flow on the Teichmueller disk of the regular octagon, cutting\n sequences and octagon continued fractions maps

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