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On the approximation of time one maps of Anosov flows by Axiom A diffeomorphisms

On the approximation of time one maps of Anosov flows by Axiom A diffeomorphisms We prove that if 𝒻1 is the time one map of a transitive and codimension one Anosov flow φ and it is C 1-approximated by Axiom A diffeomorphisms satisfying a property called P, then the flow is topologically conjugated to the suspension of a codimension one Anosov diffeomorphism. A diffeomorphism 𝒻 satisfies property P if for every periodic point in M the number of periodic points in a fundamental domain of its central manifold is constant. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of the Brazilian Mathematical Society, New Series Springer Journals

On the approximation of time one maps of Anosov flows by Axiom A diffeomorphisms

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References (14)

Publisher
Springer Journals
Copyright
Copyright © 2002 by Sociedade Brasileira de Matemática
Subject
Mathematics; Mathematics, general; Theoretical, Mathematical and Computational Physics
ISSN
1678-7544
eISSN
1678-7714
DOI
10.1007/s005740200003
Publisher site
See Article on Publisher Site

Abstract

We prove that if 𝒻1 is the time one map of a transitive and codimension one Anosov flow φ and it is C 1-approximated by Axiom A diffeomorphisms satisfying a property called P, then the flow is topologically conjugated to the suspension of a codimension one Anosov diffeomorphism. A diffeomorphism 𝒻 satisfies property P if for every periodic point in M the number of periodic points in a fundamental domain of its central manifold is constant.

Journal

Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals

Published: Apr 1, 2002

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