Double points on hyperbolic surfaces
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- by Troels Jørgensen and Hanna Sandler PDF
- Proc. Amer. Math. Soc. 119 (1993), 893-896 Request permission
Abstract:
It is shown that every proper intersection point of two closed geodesics on an orientable hyperbolic surface is either a simultaneous double point of two closed geodesics of equal length or a quadruple point, and this phenomenon persists under deformations of the surface.References
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R. Fricke and F. Klein, Vorlesungen über die Theorie der Automorphen Funktionen, Vol. 1, Teubner, Leipzig, 1897.
- Troels Jørgensen, Closed geodesics on Riemann surfaces, Proc. Amer. Math. Soc. 72 (1978), no. 1, 140–142. MR 503548, DOI 10.1090/S0002-9939-1978-0503548-2 H. Vogt, Sur les ${P_n}$ varients fundamentaux des equations differentielles lineaires du second ordre, Ann. Sci. École Norm. Sup. (3) 6 3-72.
Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 119 (1993), 893-896
- MSC: Primary 30F45; Secondary 51M10, 53A35
- DOI: https://doi.org/10.1090/S0002-9939-1993-1160302-7
- MathSciNet review: 1160302