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arXiv · 1005.1130

Nonexpanding Attractors: Conjugacy to Algebraic Models and Classification in 3-Manifolds

Aaron W. Brown
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Abstract

We prove a result motivated by Williams's classification of expanding attractors and the Franks-Newhouse Theorem on codimension-1 Anosov diffeomorphisms: If a mixing hyperbolic attractor has 1-dimensional unstable manifolds then it is either is expanding or is homeomorphic to a compact abelian group (a toral solenoid); in the latter case the dynamics is conjugate to a group automorphism. As a corollary we obtain a classification of all 2-dimensional basic sets in 3-manifolds. Furthermore we classify all hyperbolic attractors in 3-manifolds in terms of the classically studied examples, answering a question of Bonatti.

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Aaron W. Brown. 2010-05-07. Nonexpanding Attractors: Conjugacy to Algebraic Models and Classification in 3-Manifolds. https://arxiv.org/abs/1005.1130

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