Hyperbolic sub-dynamics: compact invariant 3-manifolds

2005/07/14 by Jana Rodriguez Hertz, Hertz, Jana Rodriguez
Mathematics · #37D05 #37D20 #Dynamical Systems (math.DS) #FOS: Mathematics #math.DS #msc:37D05 #msc:37D20

paper · pdf · doi:10.48550/arxiv.math/0507279

4 pages

arxiv created 2005/07/18 · arxiv updated 2009/12/01

Abstract

In 1970, Hirsch asked what kind of compact invariant sets could be part of a hyperbolic set. Here we obtain that, in case such an invariant set is a 3D manifold, it is a connected sum of tori with handles quotiented by involutions. Moreover, if the manifold is orientable, the involutions are all trivial. In 1975, Mañé characterized hyperbolic dynamics restricted to manifolds and called them quasi Anosov. We also classify here quasi-Anosov dynamics in 3D-manifolds.

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• Quasi-Anosov diffeomorphisms of 3-manifolds
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