Generic homeomorphisms have no smallest attractors

Author:
Mike Hurley

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

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Abstract: We show that if *M* is a compact manifold then there is a residual subset of the set of homeomorphisms on *M* with the property that if 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:
https://doi.org/10.1090/S0002-9939-1995-1273500-0

Keywords:
Attractor,
generic homeomorphism

Article copyright:
© Copyright 1995
American Mathematical Society