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The accessibility property of expansive geodesic flows without conjugate points

Published online by Cambridge University Press:  01 February 2008

RAFAEL OSWALDO RUGGIERO
RAFAEL OSWALDO RUGGIERO*
Affiliation:
Pontificia Universidade Católica do Rio de Janeiro, PUC-Rio, Dep. de Matemática, Rua Marqués de São Vicente 225, Gávea, Rio de Janeiro, Brazil (email: [email protected])
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Abstract

Let (M,g) be a compact, smooth Riemannian manifold without conjugate points whose geodesic flow is expansive. We show that the geodesic flow of (M,g) has the accessibility property, namely, given two points θ1, θ2 in the unit tangent bundle, there exists a continuous path joining θ1, θ2 formed by the union of a finite number of continuous curves, each of which is contained either in a strong stable set or in a strong unstable set of the dynamics. Since expansive geodesic flows of compact surfaces have no conjugate points, the accessibility property holds for every two-dimensional expansive geodesic flow.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 1 , February 2008 , pp. 229 - 244
Copyright
Copyright © Cambridge University Press 2008

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