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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Closed geodesics on a Riemann surface with application to the Markov spectrum


Authors: A. F. Beardon, J. Lehner and M. Sheingorn
Journal: Trans. Amer. Math. Soc. 295 (1986), 635-647
MSC: Primary 11F99; Secondary 11J06, 30F25
MathSciNet review: 833700
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Abstract: This paper determines those Riemann surfaces on which each nonsimple closed geodesic has a parabolic intersection--that is, an intersection in the form of a loop enclosing a puncture or a deleted disk. An application is made characterizing the simple closed geodesic on $ H/\Gamma (3)$ in terms of the Markov spectrum.

The thrust of the situation is this: If we call loops about punctures or deleted disks boundary curves, then if the surface has "little" topology, each nonsimple closed geodesic must contain a boundary curve. But if there is "enough" topology, there are nonsimple closed geodesics not containing boundary curves.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0833700-7
PII: S 0002-9947(1986)0833700-7
Article copyright: © Copyright 1986 American Mathematical Society



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