On fixed points of maps and iterated maps and applications
type: Item
instance of: scholarly article
title: On fixed points of maps and iterated maps and applications
zbMATH Open document ID: 0967.37014
DOI: 10.1016/S0362-546X(99)00111-X
author: Jörg Kampen
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-08-31T00:00:00Z
review text: The paper develops results showing that certain continuous maps from the \(n\)-cube \(I^{n}\) into \(\mathbb{R}^{n}\) have periodic points of infinitely many different minimal periods. The assumptions on the map \(f\) are that it is fixed point free, that there are relatively prime integers \(j\) and \(k\) and a set of coordinates \(C\) such that \(0\leq \pi_{i}(f^{j}(x))\leq 1\) and \(0\leq \pi_{i}(f^{k}(x))\leq 1\) for all \(x\in I^{n}\) and \(i\in C\), and that both \(f^{j}\) and \(f^{k}\) satisfy an expansive condition on each coordinate not in \(C\). Some applications to perturbations of the Hénon map, and to an economic model are indicated.
Mathematics Subject Classification ID: 37C25
Mathematics Subject Classification ID: 37N40
Mathematics Subject Classification ID: 54H25
zbMATH DE Number: 1512519
zbMATH Keywords: iterated maps
zbMATH Keywords: continuous maps
zbMATH Keywords: periodic points
zbMATH Keywords: minimal periods
zbMATH Keywords: perturbations
zbMATH Keywords: Hénon map
zbMATH Keywords: economic model
reviewed by: Mike Hurley
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1512519