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There are no minimal homeomorphisms of the multipunctured plane

Published online by Cambridge University Press:  19 September 2008

Michael Handel
Michael Handel
Affiliation:
Department of Mathematics, Lehman College, Bronx, NY 10468, USA
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Extract

The main results of this paper are the following theorem and its corollary.

Theorem 0.1. Suppose that f: S2 → S2 is an orientation-preserving homeomorphism of the two-dimensional sphere and that Fix (f) is a finite set containing at least three points. If f has a dense orbit then the number of periodic points of period n for some iterate of f grows exponentially in n.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 12 , Issue 1 , March 1992 , pp. 75 - 83
Copyright
Copyright © Cambridge University Press 1992

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References

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