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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Attractors: persistence, and density of their basins


Author: Mike Hurley
Journal: Trans. Amer. Math. Soc. 269 (1982), 247-271
MSC: Primary 58F12; Secondary 54H20, 58F10
MathSciNet review: 637037
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Abstract: An investigation of qualitative features of flows on manifolds, in terms of their attractors and quasi-attractors. A quasi-attractor is any nonempty intersection of attractors. It is shown that quasi-attractors other than attractors occur for a large set of flows. It is also shown that for a generic flow (for each flow in a residual subset of the set of all flows), each attractor "persists" as an attractor of all nearby flows. Similar statements are shown to hold with "quasi-attractor", "chain transitive attractor", and "chain transitive quasi-attractor" in place of "attractor". Finally, the set of flows under which almost all points tend asymptotically to a chain transitive quasi-attractor is characterized in terms of stable sets of invariant sets.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0637037-7
Keywords: Attractor, quasi-attractor, chain recurrence, chain transitivity
Article copyright: © Copyright 1982 American Mathematical Society