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Conformal Geometry and Dynamics

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ISSN 1088-4173

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Veech surfaces and their periodic points
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by Yoshihiko Shinomiya PDF
Conform. Geom. Dyn. 20 (2016), 176-196 Request permission

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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Additional Information
  • Yoshihiko Shinomiya
  • Affiliation: Mathematics Education, Faculty of Education College of Education, Academic Institute 836 Ohya, Suruga-ku, Shizuoka 422-8529, Japan
  • MR Author ID: 975740
  • Email: shinomiya.yoshihiko@shizuoka.ac.jp
  • Received by editor(s): July 27, 2015
  • Received by editor(s) in revised form: November 23, 2015, and March 17, 2016
  • Published electronically: May 19, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 20 (2016), 176-196
  • MSC (2010): Primary 30F35; Secondary 32G15, 32G05, 32G08
  • DOI: https://doi.org/10.1090/ecgd/296
  • MathSciNet review: 3513566