Journal of Modern Dynamics (JMD)

Axiom A diffeomorphisms derived from Anosov flows

Pages: 1 - 63, Issue 1, January 2010      doi:10.3934/jmd.2010.4.1

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Christian Bonatti - Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, BP 47 870, 21078, Dijon Cedex, France (email)
Nancy Guelman - IMERL, Facultad de Ingeniería, Universidad de La República, C.C. 30,Montevideo, Uruguay (email)

Abstract: Let $M$ be a closed $3$-manifold, and let $X_t$ be a transitive Anosov flow. We construct a diffeomorphism of the form $f(p)=Y_{t(p)}(p)$, where $Y$ is an Anosov flow equivalent to $X$. The diffeomorphism $f$ is structurally stable (satisfies Axiom A and the strong transversality condition); the non-wandering set of $f$ is the union of a transitive attractor and a transitive repeller; and $f$ is also partially hyperbolic (the direction $\RR.Y$ is the central bundle).

Keywords:  Anosov flows, AxiomA diffeomorphism, partial hyperbolicity, Birkhoff sections, perturbations.
Mathematics Subject Classification:  Primary: 37D20; Secondary: 37D30.

Received: November 2008;      Revised: January 2010;      Available Online: May 2010.