Expansive geodesic flows in manifolds with no conjugate points

RAFAEL O. RUGGIERO

doi:10.1017/S0143385797060963

Abstract

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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.

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Gomes, J Barbosa and Ruggiero, Rafael O 2007. Uniqueness of central foliations of geodesic flows for compact surfaces without conjugate points. Nonlinearity, Vol. 20, Issue. 2, p. 497.

RUGGIERO, RAFAEL OSWALDO 2008. The accessibility property of expansive geodesic flows without conjugate points. Ergodic Theory and Dynamical Systems, Vol. 28, Issue. 1, p. 229.

Ruggiero, Rafael Oswaldo 2008. A note on the divergence of geodesic rays in manifolds without conjugate points. Geometriae Dedicata, Vol. 134, Issue. 1, p. 131.

Lopes, Artur O. and Ruggiero, Rafael O. 2011. Large deviations and Aubry-Mather measures supported in nonhyperbolic closed geodesics. Discrete and Continuous Dynamical Systems, Vol. 30, Issue. 3, p. 1155.

Gelfert, Katrin and Ruggiero, Rafael O. 2019. Geodesic Flows Modelled by Expansive Flows. Proceedings of the Edinburgh Mathematical Society, Vol. 62, Issue. 1, p. 61.

Gelfert, Katrin 2019. Non-hyperbolic behavior of geodesic flows of rank 1 surfaces. Discrete and Continuous Dynamical Systems, Vol. 39, Issue. 1, p. 521.

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Liu, Fei Liu, Xiaokai and Wang, Fang 2021. On the mixing and Bernoulli properties for geodesic flows on rank 1 manifolds without focal points. Discrete and Continuous Dynamical Systems, Vol. 41, Issue. 10, p. 4791.

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Mamani, Edhin and Ruggiero, Rafael 2025. Density of Expansivity for Geodesic Flows of Compact Higher Genus Surfaces without Conjugate Points. Bulletin of the Brazilian Mathematical Society, New Series, Vol. 56, Issue. 3,

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Expansive geodesic flows in manifolds with no conjugate points

Abstract

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Expansive geodesic flows in manifolds with no conjugate points

Abstract

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