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Consequences of contractible geodesics on surfaces
Author(s):
J.
Denvir;
R.
S.
Mackay
Journal:
Trans. Amer. Math. Soc.
350
(1998),
4553-4568.
MSC (1991):
Primary 58F17
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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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
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