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Expansive geodesic flows in manifolds with no conjugate points

Published online by Cambridge University Press:  17 April 2001

RAFAEL O. RUGGIERO
RAFAEL O. RUGGIERO
Affiliation:
Dep. de Matematica, Pontificia Universidade Catolica do Rio de Janeiro, Rua Marques de Sao Vicente 225 Gávea, Rio de Janeiro, Brasil
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Abstract

Let $M$ be a compact Riemannian manifold with no conjugate points such that its geodesic flow is expansive. We show that there exists a local product structure in the unit tangent bundle of the manifold which is invariant under the geodesic flow. In particular, we have that the set of closed geodesics is dense and that the flow is topologically transitive.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 17 , Issue 1 , February 1997 , pp. 211 - 225
Copyright
1997 Cambridge University Press

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