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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Topological entropy
for geodesic flows on fibre bundles
over rationally hyperbolic manifolds


Author: Gabriel P. Paternain
Journal: Proc. Amer. Math. Soc. 125 (1997), 2759-2765
MSC (1991): Primary 58F17, 58E10
MathSciNet review: 1396992
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Abstract: Let $M$ be the total space of a fibre bundle with base a simply connected manifold whose loop space homology grows exponentially for a given coefficient field. Then we show that for any $C^{\infty }$ Riemannian metric $g$ on $M$, the topological entropy of the geodesic flow of $g$ is positive. It follows then, that there exist closed manifolds $M$ with arbitrary fundamental group, for which the geodesic flow of any $C^{\infty }$ Riemannian metric on $M$ has positive topological entropy.


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Additional Information

Gabriel P. Paternain
Affiliation: IMERL-Facultad de Ingeniería, Julio Herrera y Reissig 565, C.C. 30, Montevideo, Uruguay
Email: gabriel@cmat.edu.uy

DOI: http://dx.doi.org/10.1090/S0002-9939-97-03895-1
PII: S 0002-9939(97)03895-1
Keywords: Geodesic flow, topological entropy, loop space homology
Received by editor(s): April 6, 1995
Received by editor(s) in revised form: August 3, 1995, and March 22, 1996
Additional Notes: Supported by grants from CSIC and CONICYT
Communicated by: Mary Rees
Article copyright: © Copyright 1997 American Mathematical Society