Quasi-Anosov diffeomorphisms of 3-manifolds

Details Quasi-Anosov diffeomorphisms of 3-manifolds Quasi-Anosov diffeomorphisms of 3-manifolds

2007-09-02

arxiv.org/abs/0709.0072v1

Mathematics

Dynamical Systems

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Scientific paper

In 1969, Hirsch posed the following problem: given a diffeomorphism, and a compact invariant hyperbolic set, describe its topology and restricted dynamics. We solve the problem where the hyperbolic invariant set is a closed 3-manifold: if the manifold 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 these manifolds, called quasi-Anosov diffeomorphisms, is also classified: it is the connected sum of DA-diffeomorphisms, quotiented by commuting involutions.

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