Remarks on Sharkovsky's theorem
type: Item
instance of: scholarly article
title: Remarks on Sharkovsky's theorem
zbMATH Open document ID: 0585.58031
DOI: 10.1216/RMJ-1985-15-2-565
author: Thomas D. Rogers
published in: Rocky Mountain Journal of Mathematics
publication date: 1985-01-01T00:00:00Z
review text: When a continuous function has a cycle of given period, it has cycles of other periods specified through the Sharkovsky ordering of the positive integers. In this brief survey, the author states the Sharkovsky theorem and related results for maps of a closed interval, concentrating on simply stated conditions for the existence of certain integer periods. Continuous maps of the circle are briefly discussed and a combinatorial problem associated with the cycle structure of a set of permutations of [1,2,3,...,n] is stated.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37C10
zbMATH DE Number: 3938097
zbMATH Keywords: function on a closed interval
zbMATH Keywords: continuous function
zbMATH Keywords: Sharkovsky theorem
zbMATH Keywords: periods
zbMATH Keywords: cycle
reviewed by: A. P. Stone
MaRDI profile type: Publication
full work available at URL: rmj-1985-15-2-565
OpenAlex ID: W1969351603
description: scientific article; zbMATH DE number 3938097