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Axiom A diffeomorphisms derived from Anosov flows

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


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