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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
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2162051
Page Count: 7
You can always find the topics here!Topics: Entropy, Mathematical manifolds, Topology, Topological theorems, Myelinated nerve fibers, Mathematical theorems, Integers, Mathematical growth, Triangulation, Coefficients
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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.
Proceedings of the American Mathematical Society © 1997 American Mathematical Society