Stability of asymptotically stable sets for continuous functions
type: Item
instance of: scholarly article
title: Stability of asymptotically stable sets for continuous functions
zbMATH Open document ID: 1015.26011
DOI: 10.1016/S0022-247X(02)00438-9
author: Roy A. Mimna
author: Timothy H. Steele
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-02-11T00:00:00Z
review text: The paper deals with the problem of the behavior of asymptotically stable sets of \(f \in C(I,I)\), \(I\) a real compact interval, under small perturbations of \(f\). Let \(A(f)\) be the collection of all asymptotically stable sets of \(f\). Consider the map \(\overline A\) defined in \(C(I,I)\) so that \(\overline A(f)\) is the closure of \(A(f)\). It is shown that \(\overline A\) is lower semicontinuous at a residual set of functions in \(C(I,I)\).
Mathematics Subject Classification ID: 26A18
Mathematics Subject Classification ID: 37E05
Mathematics Subject Classification ID: 37B25
zbMATH DE Number: 1866746
zbMATH Keywords: asymptotically stable set
zbMATH Keywords: attractor
zbMATH Keywords: semicontinuity
reviewed by: Katarina Janková
MaRDI profile type: Publication
cites work: The space of $\omega $-limit sets of a continuous map of the interval
cites work: Stability in the family of \(\omega \)-limit sets of continuous maps of the interval
cites work: Q4331836
cites work: Points generating the principal measure of chaos
cites work: The space of dynamical systems with the \(C^ 0\)-topology
cites work: Measures of Chaos and a Spectral Decomposition of Dynamical Systems on the Interval
cites work: Iterative stability in the class of continuous functions
cites work: Continuity structure of \(f\mapsto \cup _{x\in I}\omega (x,f)\) and \(f\mapsto \{\omega (x,f) : x\in I\}\)
cites work: Q5621780
description: scientific article; zbMATH DE number 1866746