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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Generic homeomorphisms have no smallest attractors


Author: Mike Hurley
Journal: Proc. Amer. Math. Soc. 123 (1995), 1277-1280
MSC: Primary 58F12
MathSciNet review: 1273500
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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

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1273500-0
PII: S 0002-9939(1995)1273500-0
Keywords: Attractor, generic homeomorphism
Article copyright: © Copyright 1995 American Mathematical Society