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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

An embedding theorem for homeomorphisms of the closed disc


Author: Gary D. Jones
Journal: Proc. Amer. Math. Soc. 26 (1970), 352-354
MSC: Primary 54.82
DOI: https://doi.org/10.1090/S0002-9939-1970-0263059-1
MathSciNet review: 0263059
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Abstract: If $ f$ is an orientation preserving self-homeomorphism of the closed disc $ D$ with the property that if $ x,y \in D - N$, where the set of fixed points $ N$ is finite and contained in $ D - \operatorname{int} D$, then there exists an arc $ A \subset D - N$ joining $ x$ and $ y$ such that $ {f^n}(A)$ tends to a fixed point as $ n \to \pm \infty $, then it is shown that $ f$ can be embedded in a continuous flow on $ D$.


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DOI: https://doi.org/10.1090/S0002-9939-1970-0263059-1
Keywords: Embedding, discrete flows, continuous flows, homeomorphisms, closed disc
Article copyright: © Copyright 1970 American Mathematical Society