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ISSN 1088-6850(e) ISSN 0002-9947(p)

Quasi-Anosov diffeomorphisms of 3-manifolds

Author(s): T. Fisher; M. Rodriguez Hertz
Journal: Trans. Amer. Math. Soc. 361 (2009), 3707-3720.
MSC (2000): Primary 37D05, 37D20
Posted: February 10, 2009
MathSciNet review: 2491896
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Abstract: In 1969, Hirsch posed the following problem: given a diffeomorphism $f:N\to N$ and a compact invariant hyperbolic set $\Lambda$ of , describe the topology of $\Lambda$ and the dynamics of restricted to $\Lambda$ . We solve the problem where $\Lambda=M^3$ is a closed -manifold: if is orientable, then it is a connected sum of tori and handles; otherwise it is a connected sum of tori and handles quotiented by involutions.

The dynamics of the diffeomorphisms restricted to , called quasi-Anosov diffeomorphisms, is also classified: it is the connected sum of DA-diffeomorphisms, quotiented by commuting involutions.

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