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A sufficient condition for robustly minimal foliations

Published online by Cambridge University Press:  13 January 2006

ENRIQUE R. PUJALS  and
MARTÍN SAMBARINO
ENRIQUE R. PUJALS
Affiliation:
IMPA, Estrada Dona Castorina 110, CP 22460-320, Rio de Janeiro, Brazil (e-mail: enrique@impa.br)
MARTÍN SAMBARINO
Affiliation:
Centro de Matemática, Fac. de Ciencias, Iguá 4225, CP 11.400, Montevideo, Uruguay (e-mail: samba@cmat.edu.uy)
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Abstract

Let $f:M\to M$ be a partially hyperbolic diffeomorphism, ${\it TM}=E^{ss}\oplus E^c\oplus E^{uu}$ such that the stable foliation $\mathcal{F}^{ss}(f)$ is minimal. We give a sufficient condition so that this foliation remains minimal after perturbations, i.e. $\mathcal{F}^{ss}(g)$ is minimal for every g sufficiently close to f.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 1 , February 2006 , pp. 281 - 289
Copyright
2006 Cambridge University Press

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