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Topological Entropy for Geodesic Flows on Fibre Bundles Over Rationally Hyperbolic Manifolds

Gabriel P. Paternain
Proceedings of the American Mathematical Society
Vol. 125, No. 9 (Sep., 1997), pp. 2759-2765
Stable URL: http://www.jstor.org/stable/2162051
Page Count: 7
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Topological Entropy for Geodesic Flows on Fibre Bundles Over Rationally Hyperbolic Manifolds
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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∞ 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∞ Riemannian metric on M has positive topological entropy.

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