Hostname: page-component-7b7567c8c-kwt9d Total loading time: 0 Render date: 2026-11-14T04:15:30.937Z Has data issue: false hasContentIssue false
  • English
  • Français

The ordering on permutations induced by continuous maps of the real line

Published online by Cambridge University Press:  19 September 2008

Chris Bernhardt
Chris Bernhardt
Affiliation:
Department of Mathematics, Lafayette College, Easton, PA 18042, USA
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

Continuous maps from the real line to itself give, in a natural way, a partial ordering of permutations. This ordering restricted to cycles is studied.

Necessary and sufficient conditions are given for a cycle to have an immediate predecessor. When a cycle has an immediate predecessor it is unique; it is shown how to construct it. Every cycle has immediate successors; it is shown how to construct them.

Information

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 7 , Issue 2 , June 1987, pp. 155 - 160
Copyright
Copyright © Cambridge University Press 1987

References

REFERENCES

[1]Alseda, L., Llibre, J. & Serra, R.. Minimal periodic orbits for continuous maps of the interval. Trans. Amer. Math. Soc. 286 (1984), 595–627.CrossRefGoogle Scholar
[2]Baldwin, S.. Generalizations of a theorem of Sarkovskii on orbits of continuous real-valued functions. Preprint.Google Scholar
[3]Bernhardt, C.. Simple permutations with order a power of two. Ergod. Th. & Dynam. Sys. (1984), 4, 179–186.CrossRefGoogle Scholar
[4]Ho, C. W.. On the structure of minimum orbits of periodic points for maps of the real line. Preprint.Google Scholar