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Topological stability and Gromov hyperbolicity

Published online by Cambridge University Press:  01 February 1999

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, Brasil (e-mail: rorr@saci.mat.puc.rio.br)
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Abstract

We show that if the geodesic flow of a compact analytic Riemannian manifold $M$ of non-positive curvature is either $C^{k}$-topologically stable or satisfies the $\epsilon$-$C^{k}$-shadowing property for some $k > 0$ then the universal covering of $M$ is a Gromov hyperbolic space. The same holds for compact surfaces without conjugate points.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 1 , February 1999 , pp. 143 - 154
Copyright
1999 Cambridge University Press

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