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ISOTOPY STABLE DYNAMICS RELATIVE TO COMPACT INVARIANT SETS

Published online by Cambridge University Press:  01 November 1999

PHILIP BOYLAND  and
TOBY HALL
PHILIP BOYLAND
Affiliation:
Department of Mathematics, University of Florida, PO Box 118105, Gainesville, FL 32611-8105, U.S.A., email:[email protected]
TOBY HALL
Affiliation:
Department of Mathematical Sciences University of Liverpool, Liverpool L69 3BX, email:[email protected]
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Abstract

Let $f$ be an orientation-preserving homeomorphism of a compact orientable manifold. Sufficient conditions are given for the persistence of a collection of periodic points under isotopy of $f$ relative to a compact invariant set $A$. Two main applications are described. In the first,~$A$ is the closure of a single discrete orbit of~$f$, and~$f$ has a Smale horseshoe, all of whose periodic orbits persist; in the second,~$A$ is a minimal invariant Cantor set obtained as the limit of a sequence of nested periodic orbits, all of which are shown to persist under isotopy relative to~$A$.

1991 Mathematics Subject Classification: 58F20, 58F15.

Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 79 , Issue 3 , November 1999 , pp. 673 - 693
Copyright
1999 London Mathematical Society

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