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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Billiards and Teichmüller curves on Hilbert modular surfaces


Author: Curtis T. McMullen
Journal: J. Amer. Math. Soc. 16 (2003), 857-885
MSC (2000): Primary 32G15; Secondary 37D50, 11F41, 14G35
Published electronically: June 19, 2003
MathSciNet review: 1992827
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Abstract: 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

DOI: http://dx.doi.org/10.1090/S0894-0347-03-00432-6
PII: S 0894-0347(03)00432-6
Received by editor(s): April 8, 2002
Published electronically: June 19, 2003
Additional Notes: Research supported in part by the NSF
Article copyright: © Copyright 2003 American Mathematical Society