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

Authors:
J. Lehner and M. Sheingorn

Journal:
Math. Comp. **44** (1985), 233-240

MSC:
Primary 11F06; Secondary 11J06, 20H10, 30F35

DOI:
https://doi.org/10.1090/S0025-5718-1985-0771045-7

MathSciNet review:
771045

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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.

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DOI:
https://doi.org/10.1090/S0025-5718-1985-0771045-7

Article copyright:
© Copyright 1985
American Mathematical Society