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Transitive Anosov flows and Axiom-A diffeomorphisms

Published online by Cambridge University Press:  01 June 2009

CHRISTIAN BONATTI  and
NANCY GUELMAN
CHRISTIAN BONATTI
Affiliation:
Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, BP 47 870, 21078, Dijon Cedex, France (email: bonatti@u-bourgogne.fr)
NANCY GUELMAN
Affiliation:
IMERL, Facultad de Ingeniería, Universidad de La República, C.C. 30, Montevideo, Uruguay (email: nguelman@fing.edu.uy)
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Abstract

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Let M be a smooth compact Riemannian manifold without boundary, and ϕ:M×ℝ→M a transitive Anosov flow. We prove that if the time-one map of ϕ is C1-approximated by Axiom-A diffeomorphisms with more than one attractor, then ϕ is topologically equivalent to the suspension of an Anosov diffeomorphism.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 29 , Issue 3 , June 2009 , pp. 817 - 848
Copyright
Copyright © Cambridge University Press 2008

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