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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Fixed points of pointwise almost periodic homeomorphisms on the two-sphere


Author: W. K. Mason
Journal: Trans. Amer. Math. Soc. 202 (1975), 243-258
MSC: Primary 54H25
DOI: https://doi.org/10.1090/S0002-9947-1975-0362280-0
MathSciNet review: 0362280
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Abstract: A homeomorphism $ f$ of the two-sphere $ {S^2}$ onto itself is defined to be pointwise almost periodic (p.a.p.) if the collection of orbit closures forms a decomposition of $ {S^2}$. It is shown that if $ f:{S^2} \to {S^2}$ is p.a.p. and orientation-reversing then the set of fixed points of $ f$ is either empty or a simple closed curve; if $ f:{S^2} \to {S^2}$ is p.a.p. orientation-preserving and has a finite number of fixed points, then $ f$ is shown to have exactly two fixed points.


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DOI: https://doi.org/10.1090/S0002-9947-1975-0362280-0
Keywords: Pointwise almost periodic transformation, recurrent point, prime ends, periodic transformation
Article copyright: © Copyright 1975 American Mathematical Society