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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
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Abstract

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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.

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

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