Period three plays a negative role in a multivalued version of Sharkovskii's theorem
type: Item
instance of: scholarly article
title: Period three plays a negative role in a multivalued version of Sharkovskii's theorem
zbMATH Open document ID: 1015.37032
DOI: 10.1016/S0362-546X(01)00876-8
author: Jan Andres
author: Libor Jüttner
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-11-28T00:00:00Z
review text: This paper deals with periodic orbits of iterated multivalued maps \({\mathbb{R}}\multimap {\mathbb{R}}\) with nonempty values. For such maps, opposite to the case of the classical Sharkovskii's theorem, a \(3\)-orbit does not necessarily imply the existence of a \(2\)-orbit. However, the authors prove the following proposition: Assume that a multivalued upper semicontinuous mapping \(\varphi:{\mathbb{R}}\to 2^{\mathbb{R}}\setminus \{\emptyset\}\), whose values are either single points or closed intervals, has no primary \(3\)-orbit and admits an \(n\)-orbit for \(n\neq 1\). Then \(\varphi\) admits a \(2\)-orbit.
reviewed by: Marco Spadini
Mathematics Subject Classification ID: 37E15
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 1836633
zbMATH Keywords: Sharkowskii's theorem: multivalued version
zbMATH Keywords: \(2\)-orbits
MaRDI profile type: Publication
cites work: On a multivalued version of the Sharkovskii theorem and its application to differential inclusions
cites work: A Simple Special Case of Sharkovskii's Theorem
cites work: Q3836181
cites work: Period Three Implies Chaos
cites work: Q4888828
cites work: Q3744882
full work available at URL: s0362-546x(01)00876-8
OpenAlex ID: W1988980985
description: scientific article; zbMATH DE number 1836633