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

DOI:
https://doi.org/10.1090/S0002-9947-1982-0637037-7

MathSciNet review:
637037

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Abstract | References | Similar Articles | Additional Information

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0637037-7

Keywords:
Attractor,
quasi-attractor,
chain recurrence,
chain transitivity

Article copyright:
© Copyright 1982
American Mathematical Society