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Accessible saddles on fractal basin boundaries

Published online by Cambridge University Press:  19 September 2008

Kathleen T. Alligood  and
James A. Yorke
Kathleen T. Alligood
Affiliation:
Department of Mathematics, George Mason University, Fairfax, VA 22030, USA
James A. Yorke
Affiliation:
Department of Mathematics and Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, USA
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Abstract

For a homeomorphism of the plane, the basin of attraction of a fixed point attractor is open, connected, and simply-connected, and hence is homeomorphic to an open disk. The basin boundary, however, need not be homeomorphic to a circle. When it is not, it can contain periodic orbits of infinitely many different periods.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 3 , September 1992 , pp. 377 - 400
Copyright
Copyright © Cambridge University Press 1992

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References

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