Remote Access Proceedings of the American Mathematical Society
Green Open Access

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
Full-text PDF

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$.


References [Enhancements On Off] (What's this?)

  • [1] S. A. Andrea, On homeomorphisms of the plane which have no fixed points, Abh. Math. Sem. Univ. Hamburg 30 (1967), 61-74. MR 34 #8397. MR 0208588 (34:8397)
  • [2] N. J. Fine and G. E. Schweigert, On the group of homeomorphisms of an arc, Ann. of Math. (2) 62 (1955), 237-253. MR 17, 288. MR 0072460 (17:288b)
  • [3] N. E. Foland, An embedding theorem for discrete flows on a closed $ 2$-cell, Duke Math. J. 33 (1966), 441-444. MR 33 #6609. MR 0198451 (33:6609)
  • [4] -, An embedding theorem for contracting homeomorphisms, Math. Systems Theory 3 (1969), 166-169. MR 0248795 (40:2045)
  • [5] N. E. Foland and W. R. Utz, The embedding of discrete flows in continuous flows, Proc. Internat. Sympos. Ergodic Theory (Tulane Univ., New Orleans, La., 1961), Academic Press, New York, 1963, pp. 121-134. MR 28 #3412. MR 0160198 (28:3412)
  • [6] M. K. Fort, Jr., The embedding of homeomorphisms inflows, Proc. Amer. Math. Soc. 6 (1955), 960-967. MR 18, 326. MR 0080911 (18:326b)
  • [7] W. H. Gottschalk, Minimal sets: an introduction to topological dynamics, Bull. Amer. Math. Soc. 64 (1958), 336-351. MR 20 #6484. MR 0100048 (20:6484)
  • [8] W. H. Gottschalk and G. A. Hedlund, Topological dynamics, Amer. Math. Soc. Colloq. Publ., vol. 36, Amer. Math. Soc., Providence, R. I., 1955. MR 17, 650. MR 0074810 (17:650e)
  • [9] G. D. Jones, The embedding of flows inflows, Ph.D. Thesis, Univ. of Missouri, Columbia, 1969.
  • [10] W. R. Utz, The embedding of a linear discrete flow in a continuous flow, Colloq. Math. 15 (1966), 263-270. MR 34 #2000. MR 0202126 (34:2000)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 54.82

Retrieve articles in all journals with MSC: 54.82


Additional Information

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

American Mathematical Society