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A class of C∞-stable foliations

Published online by Cambridge University Press:  19 September 2008

Aziz El Kacimi Alaoui  and
Marcel Nicolau
Aziz El Kacimi Alaoui
Affiliation:
URA au CNRS 751, Université de Valenciennes, 59326 Valenciennes Cedex, France
Marcel Nicolau
Affiliation:
Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra, Spain
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Abstract

We consider foliations F obtained as the suspension of a linear foliation F0 on n by means of a linear Anosov diffeomorphism A of n keeping F0 invariant. Under suitable conditions on A the foliations F are shown to be C∞-stable, i.e. any differentiable foliation which is C∞-close to F is C∞-conjugated to F. The proof relies on a criterium of stability stated by R. Hamilton.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 13 , Issue 4 , December 1993 , pp. 697 - 704
Copyright
Copyright © Cambridge University Press 1993

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