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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Attractors: persistence, and density of their basins
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by Mike Hurley PDF
Trans. Amer. Math. Soc. 269 (1982), 247-271 Request permission

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
  • © Copyright 1982 American Mathematical Society
  • 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