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An extension of Šarkovskiư's Theorem to the n-od

Published online by Cambridge University Press:  19 September 2008

Stewart Baldwin
Stewart Baldwin
Affiliation:
Division of Mathematics, Auburn University, Auburn, AL 36849–5310, USA
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Abstract

The n-od is defined to be the set of all complex numbers z such that zn is a real number in the interval [0,1], i.e., a central point with n copies of the unit interval attached at their endpoints. Given a space X and a function f:X → X, Per (f) is defined to be the set {k: f has for a point of (least) period k, k a positive integer}. The main result of this paper is to give, for each n, a complete characterization of all possible sets Per (f), where f ranges over all continuous functions on the n-od.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 2 , June 1991 , pp. 249 - 271
Copyright
Copyright © Cambridge University Press 1991

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