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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Generic homeomorphisms have no smallest attractors
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by Mike Hurley PDF
Proc. Amer. Math. Soc. 123 (1995), 1277-1280 Request permission

Abstract:

We show that if M is a compact manifold then there is a residual subset $\mathcal {R}$ of the set of homeomorphisms on M with the property that if $f \in \mathcal {R}$ then f has no smallest attractor (that is, an attractor with the property that none of its proper subsets is also an attractor). Part of the motivation for this result comes from portions of a recent paper by Lewowicz and Tolosa that deal with properties of smallest attractors of generic homeomorphisms.
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 1277-1280
  • MSC: Primary 58F12
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1273500-0
  • MathSciNet review: 1273500