Inverse map characterization of asymptotic stability on the line
type: Item
instance of: scholarly article
title: Inverse map characterization of asymptotic stability on the line
zbMATH Open document ID: 0988.37057
author: Hassan Sedaghat
published in: Rocky Mountain Journal of Mathematics
publication date: 2002-07-14T00:00:00Z
full work available at URL: CONT29-4.html
review text: This paper studies the asymptotic stability in which continuous mapping \(f\) is compared to its inverse \(f^{-1}\) in a cut-and-paste sort of way. The author presents a necessary and sufficient condition for asymptotic stability. More precisely, the author proves that a fixed point \(x_*\) is asymptotically stable if and only if the inverse image of the part of \(f\) to the right of \(x_*\) lies in the region of the plane that is above both the identity line and the part of \(f\) to the left of \(x_*\). Moreover, the author presents an application of the criterion mentioned above.
Mathematics Subject Classification ID: 37E99
zbMATH DE Number: 1455482
zbMATH Keywords: isolated fixed point
zbMATH Keywords: stability
zbMATH Keywords: asymptotic stability
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
OpenAlex ID: W2030988012
cites work: Q3137926
cites work: Q3997807
cites work: The Impossibility of Unstable, Globally Attracting Fixed Points for Continuous Mappings of the Line
cites work: Stable Orbits and Bifurcation of Maps of the Interval
DOI: 10.1216/RMJM/1181070419
description: scientific article; zbMATH DE number 1455482