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Pseudocircles, diffeomorphisms and perturbable dynamical systems*

Published online by Cambridge University Press:  14 October 2010

Judy A. Kennedy  and
James A. Yorke
Judy A. Kennedy
Affiliation:
Department of Mathematical Sciences, University of Delaware, Newark, DE19716, USA
James A. Yorke
Affiliation:
Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
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Abstract

We construct an example of a C∞ diffeomorphism on a 7-manifold which has an invariant set with an uncountable number of pseudocircle components. Furthermore, any diffeomorphism which is sufficiently close (in the C1 metric) to the constructed map has a similar invariant set. We also discuss the topological nature of the invariant set.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 16 , Issue 5 , October 1996 , pp. 1031 - 1057
Copyright
Copyright © Cambridge University Press 1996

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