Veech surfaces and their periodic points

Shinomiya, Yoshihiko

doi:10.1090/ecgd/296

Veech surfaces and their periodic points
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by Yoshihiko Shinomiya

Conform. Geom. Dyn. 20 (2016), 176-196

DOI: https://doi.org/10.1090/ecgd/296

Published electronically: May 19, 2016

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Abstract:

We give inequalities comparing widths or heights of cylinder decompositions of Veech surfaces with the signatures of their Veech groups. As an application of these inequalities, we estimate the numbers of periodic points of non-arithmetic Veech surfaces. The upper bounds depend only on the topological types of Veech surfaces and the signatures of Veech groups as Fuchsian groups. The upper bounds also estimate the numbers of holomorphic sections of holomorphic families of Riemann surfaces constructed from Veech groups of non-arithmetic Veech surfaces.

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