American Institute of Mathematical Sciences

January  2010, 4(1): 1-63. doi: 10.3934/jmd.2010.4.1

Axiom A diffeomorphisms derived from Anosov flows

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

Received  November 2008 Revised  January 2010 Published  May 2010

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).
Citation: Christian Bonatti, Nancy Guelman. Axiom A diffeomorphisms derived from Anosov flows. Journal of Modern Dynamics, 2010, 4 (1) : 1-63. doi: 10.3934/jmd.2010.4.1
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