The ordering on permutations induced by continuous maps of the real line
- 1 June 1987
- journal article
- research article
- Published by Cambridge University Press (CUP) in Ergodic Theory and Dynamical Systems
- Vol. 7 (2) , 155-160
- https://doi.org/10.1017/s0143385700003898
Abstract
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.Keywords
This publication has 2 references indexed in Scilit:
- Minimal Periodic Orbits for Continuous Maps of the IntervalTransactions of the American Mathematical Society, 1984
- Simple permutations with order a power of twoErgodic Theory and Dynamical Systems, 1984