Computing self-intersections of closed geodesics on finite-sheeted covers of the modular surface-Reference-Cited by-同舟云学术

Computing self-intersections of closed geodesics on finite-sheeted covers of the modular surface

Published:1985 Issue:169 Volume:44 Page:233-240
ISSN:0025-5718
Container-title:Mathematics of Computation
language:en
Short-container-title:Math. Comp.

Author:

Lehner J.,Sheingorn M.

Abstract

An algorithm is given for deciding whether a closed geodesic on a finite-sheeted cover of the modular surface has self-intersections; if it does, the algorithm gives them in the order they occur in traversing the geodesic. The following general result on geodesics is proved: any closed geodesic on a Riemann surface R can be lifted to a simple closed geodesic on some finite-sheeted cover of R. In the last two sections the connection with the stabilizer (under the modular group) of a Markov quadratic irrationality is discussed.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Link

http://www.ams.org/mcom/1985-44-169/S0025-5718-1985-0771045-7/S0025-5718-1985-0771045-7.pdf

Reference10 articles.

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2. A. F. Beardon, J. Lehner & M. Sheingorn, "Closed simple geodesics on Riemann surfaces and the Markov spectrum." (To be published.)

3. An algorithm for simple curves on surfaces;Birman, Joan S.;J. London Math. Soc. (2),1984

4. J. Birman & C. Series, "Simple curves have Hausdorff dimension one." (Preprint.)

5. Cambridge Tracts in Mathematics and Mathematical Physics, No. 45;Cassels, J. W. S.,1957

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