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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Billiards and Teichmüller curves on Hilbert modular surfaces
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by Curtis T. McMullen PDF
J. Amer. Math. Soc. 16 (2003), 857-885 Request permission


This paper exhibits an infinite collection of algebraic curves isometrically embedded in the moduli space of Riemann surfaces of genus two. These Teichmüller curves lie on Hilbert modular surfaces parameterizing Abelian varieties with real multiplication. Explicit examples, constructed from L-shaped polygons, give billiard tables with optimal dynamical properties.
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Additional Information
  • Curtis T. McMullen
  • Affiliation: Mathematics Department, Harvard University, 1 Oxford Street, Cambridge, Massachusetts 02138-2901
  • Received by editor(s): April 8, 2002
  • Published electronically: June 19, 2003
  • Additional Notes: Research supported in part by the NSF
  • © Copyright 2003 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 16 (2003), 857-885
  • MSC (2000): Primary 32G15; Secondary 37D50, 11F41, 14G35
  • DOI:
  • MathSciNet review: 1992827