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Closed Geodesics on a Riemann Surface With Application to the Markov Spectrum
A. F. Beardon, J. Lehner and M. Sheingorn
Transactions of the American Mathematical Society
Vol. 295, No. 2 (Jun., 1986), pp. 635-647
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2000055
Page Count: 13
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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/Γ(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.
Transactions of the American Mathematical Society © 1986 American Mathematical Society