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MINIMALITY OF STRONG STABLE AND UNSTABLE FOLIATIONS FOR PARTIALLY HYPERBOLIC DIFFEOMORPHISMS

Published online by Cambridge University Press:  14 October 2002

Christian Bonatti ,
Lorenzo J. Díaz  and
Raúl Ures
Christian Bonatti
Affiliation:
Laboratoire de Topologie, UMR 5584 du CNRS, BP 47 870, 21078 Dijon Cedex, France (bonatti@satieu-bourgogne.fr)
Lorenzo J. Díaz
Affiliation:
Departamento Matemática, PUC-Rio, Marquês de S. Vicente 225, 22453-900 Rio de Janeiro RJ, Brazil (lodiaz@mat.puc-rio.br)
Raúl Ures
Affiliation:
CC 30 IMERL, Facultad de Ingenierí a, Universidad de la República, Montevideo, Uruguay (ures@fing.edu.uy)
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Abstract

We give a topological criterion for the minimality of the strong unstable (or stable) foliation of robustly transitive partially hyperbolic diffeomorphisms.

As a consequence we prove that, for $3$-manifolds, there is an open and dense subset of robustly transitive diffeomorphisms (far from homoclinic tangencies) such that either the strong stable or the strong unstable foliation is robustly minimal.

We also give a topological condition (existence of a central periodic compact leaf) guaranteeing (for an open and dense subset) the simultaneous minimality of the two strong foliations.

AMS 2000 Mathematics subject classification: Primary 37D25; 37C70; 37C20; 37C29

Keywords

minimal foliationpartial hyperbolicitystrong stable and unstable foliationstransitive
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 1 , Issue 4 , October 2002 , pp. 513 - 541
Copyright
2002 Cambridge University Press

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