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Transitivity of codimension-one Anosov actions of ℝk on closed manifolds

Published online by Cambridge University Press:  18 January 2010

THIERRY BARBOT  and
CARLOS MAQUERA
THIERRY BARBOT
Affiliation:
CNRS, UMR 5669, UMPA, ENS Lyon 46, allée d’Italie 69364 Lyon, France (email: [email protected]) LANLG, Université d’Avignon, 33, rue Louis Pasteur, 84000 Avignon, France (email: [email protected])
CARLOS MAQUERA
Affiliation:
Universidade de São Paulo - São Carlos, Instituto de ciências matemáticas e de Computação, Av. do Trabalhador São-Carlense 400, 13560-970 São Carlos, SP, Brazil (email: [email protected])
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Abstract

We consider Anosov actions of ℝk, k≥2, on a closed connected orientable manifold M, of codimension one, i.e. such that the unstable foliation associated to some element of ℝk has dimension one. We prove that if the ambient manifold has dimension greater than k+2, then the action is topologically transitive. This generalizes a result of Verjovsky for codimension-one Anosov flows.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 1 , February 2011 , pp. 1 - 22
Copyright
Copyright © Cambridge University Press 2009

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