Abstract
AbstractThe 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.
Publisher
Cambridge University Press (CUP)
Subject
Applied Mathematics,General Mathematics
Reference14 articles.
1. A topologist's view of Šharkovsky's Theorem;Schirmer;Houston J. Math.,1985
2. The ordering on permutations induced by continuous maps of the real line
3. Periodic points of small periods of continuous mappings of trees;Imrich;Ann. Discr. Math.,1985
4. Periodic Orbits of Maps of Y
Cited by
52 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. Coexistence of Cycles for One-Dimensional Spaces;SpringerBriefs in Mathematics;2022
2. One-dimensional dynamical systems;Russian Mathematical Surveys;2021-10-01
3. On the set of periods of sigma maps of degree 1;Discrete & Continuous Dynamical Systems - A;2015
4. The period set of a map from the Cantor set to itself;Discrete & Continuous Dynamical Systems - A;2013
5. A Sharkovsky theorem for non-locally connected spaces;Discrete and Continuous Dynamical Systems;2012-05