Axiom Adiffeomorphisms derived from Anosov flows

Christian Bonatti; Nancy Guelman

doi:10.3934/jmd.2010.4.1

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2010, Volume 4, Issue 1: 1-63. Doi: 10.3934/jmd.2010.4.1

This issue Previous Article Next Article The Ricci flow for nilmanifolds

Axiom A diffeomorphisms derived from Anosov flows

Christian Bonatti^1, and
Nancy Guelman^2,

1.
Université de Bourgogne, Institut de Mathématiques de Bourgogne, UMR 5584 du CNRS, BP 47 870, 21078, Dijon Cedex
2.
IMERL, Facultad de Ingeniería, Universidad de La República, C.C. 30,Montevideo

Received: October 31, 2008

Revised: December 31, 2009

Published: April 2010

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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).

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Mathematics Subject Classification: Primary: 37D20; Secondary: 37D30.

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