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 | References | Similar Articles | Additional Information
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 $D$.
- Stephen A. Andrea, On homoeomorphisms of the plane which have no fixed points, Abh. Math. Sem. Univ. Hamburg 30 (1967), 61–74. MR 208588, DOI https://doi.org/10.1007/BF02993992
- N. J. Fine and G. E. Schweigert, On the group of homeomorphisms of an arc, Ann. of Math. (2) 62 (1955), 237–253. MR 72460, DOI https://doi.org/10.2307/1969678
- N. E. Foland, An embedding theorem for discrete flows on a closed 2-cell, Duke Math. J. 33 (1966), 441–444. MR 198451
- N. E. Foland, An embedding theorem for contracting homeomorphisms, Math. Systems Theory 3 (1969), 166–169. MR 248795, DOI https://doi.org/10.1007/BF01746524
- N. E. Foland and W. R. Utz, The embedding of discrete flows in continuous flows, Ergodic Theory (Proc. Internat. Sympos., Tulane Univ., New Orleans, La., 1961) Academic Press, New York, 1963, pp. 121–134. MR 0160198
- M. K. Fort Jr., The embedding of homeomorphisms in flows, Proc. Amer. Math. Soc. 6 (1955), 960–967. MR 80911, DOI https://doi.org/10.1090/S0002-9939-1955-0080911-2
- W. H. Gottschalk, Minimal sets: an introduction to topological dynamics, Bull. Amer. Math. Soc. 64 (1958), 336–351. MR 100048, DOI https://doi.org/10.1090/S0002-9904-1958-10223-2
- Walter Helbig Gottschalk and Gustav Arnold Hedlund, Topological dynamics, American Mathematical Society Colloquium Publications, Vol. 36, American Mathematical Society, Providence, R. I., 1955. MR 0074810 G. D. Jones, The embedding of flows inflows, Ph.D. Thesis, Univ. of Missouri, Columbia, 1969.
- W. R. Utz, The embedding of a linear discrete flow in a continuous flow, Colloq. Math. 15 (1966), 263–270. MR 202126, DOI https://doi.org/10.4064/cm-15-2-263-270
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Keywords:
Embedding,
discrete flows,
continuous flows,
homeomorphisms,
closed disc
Article copyright:
© Copyright 1970
American Mathematical Society