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

 

Consequences of contractible geodesics
on surfaces


Authors: J. Denvir and R. S. Mackay
Journal: Trans. Amer. Math. Soc. 350 (1998), 4553-4568
MSC (1991): Primary 58F17
MathSciNet review: 1615951
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Abstract: The geodesic flow of any Riemannian metric on a geodesically convex surface of negative Euler characteristic is shown to be semi-equivalent to that of any hyperbolic metric on a homeomorphic surface for which the boundary (if any) is geodesic. This has interesting corollaries. For example, it implies chaotic dynamics for geodesic flows on a torus with a simple contractible closed geodesic, and for geodesic flows on a sphere with three simple closed geodesics bounding disjoint discs.


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Additional Information

J. Denvir
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
Address at time of publication: Department of Mathematics, Truman State University, Kirksville, Missouri 63501
Email: jdenvir@math.truman.edu

R. S. Mackay
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, UK
Address at time of publication: DAMTP, Silver Street, University of Cambridge, CB3 9EW, U.K.
Email: R.S.MacKay@damtp.cam.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02340-X
PII: S 0002-9947(98)02340-X
Keywords: Geodesics, semiconjugacy, surface, dynamics
Received by editor(s): September 7, 1995
Received by editor(s) in revised form: September 13, 1996
Article copyright: © Copyright 1998 American Mathematical Society