Topological entropy for geodesic flows on fibre bundles over rationally hyperbolic manifolds
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- by Gabriel P. Paternain PDF
- Proc. Amer. Math. Soc. 125 (1997), 2759-2765 Request permission
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.References
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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
- 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
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2759-2765
- MSC (1991): Primary 58F17, 58E10
- DOI: https://doi.org/10.1090/S0002-9939-97-03895-1
- MathSciNet review: 1396992