The dynamics of generic Kuperberg flows

In this work, we study the dynamical properties of Krystyna Kuperberg's aperiodic flows on \(3\)-manifolds. We introduce the notion of a ``zippered lamination'', and with suitable generic hypotheses, show that the unique minimal set for such a flow is an invariant zippered lamination....

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Bibliographic Details
Published in:arXiv.org 2015-10
Main Authors: Hurder, Steven, Rechtman, Ana
Format: Article
Language:English
Subjects:
Chaos theory
Homology
Invariants
Topology
Online Access:Get full text
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Summary:In this work, we study the dynamical properties of Krystyna Kuperberg's aperiodic flows on \(3\)-manifolds. We introduce the notion of a ``zippered lamination'', and with suitable generic hypotheses, show that the unique minimal set for such a flow is an invariant zippered lamination. We obtain a precise description of the topology and dynamical properties of the minimal set, including the presence of non-zero entropy-type invariants and chaotic behavior. Moreover, we show that the minimal set does not have stable shape, yet satisfies the Mittag-Leffler condition for homology groups.
ISSN:2331-8422