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The topology of attractors

Published online by Cambridge University Press:  14 October 2010

Judy A. Kennedy
Judy A. Kennedy
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, De 19716, USA, (e-mail: [email protected])
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Abstract

We prove for a large class of compact metric spaces, including those manifolds of dimension at least two, Hilbert cube manifolds, and homogeneous Menger manifolds, that ‘most’ self-homeomorphisms (in the sense of residual set of homeomorphisms) have certain properties. Specifically, if F: X → X is one of these homeomorphisms, then F admits

• a dense, open wandering set;

• a nowhere dense chain recurrent set;

• an infinite collection of attractors (and repellers), each of which has nonempty interior and cannot be reduced to a ‘smallest’ attractor (or ‘largest’ repeller); and an uncountable collection of pairwise disjoint quasi-attractors.

We also discuss the topology of the boundaries of attractors.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 6 , December 1996 , pp. 1311 - 1322
Copyright
Copyright © Cambridge University Press 1996

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References

REFERENCES

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