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There are no minimal homeomorphisms of the multipunctured plane. (English) Zbl 0769.58037
The author proves the following theorem and its corollary.
Theorem. Suppose that $$f: S^ 2 \to S^ 2$$ is an orientation-preserving homeomorphism of the two-dimensional sphere and that $$\text{Fix}(f)$$ 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 $$n$$.
Corollary. There are no minimal homeomorphisms of the multipunctured plane $$\mathbb{R}^ 2\setminus K$$ where $$K$$ is a finite set with at least two points.
Reviewer: Y.Kozai (Tokyo)

##### MSC:
 37A99 Ergodic theory 58D05 Groups of diffeomorphisms and homeomorphisms as manifolds
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##### References:
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