Topological properties of prolongations and stable sets for semigroup actions
type: Item
instance of: scholarly article
title: Topological properties of prolongations and stable sets for semigroup actions
zbMATH Open document ID: 1469.37010
author: Victor H. L. Rocha
author: Ronan A. Reis
published in: Topology and its Applications
publication date: 2021-03-09T00:00:00Z
review text: The authors investigate topological properties of Lyapunov stable sets for semigroup actions on Tychonoff spaces. Under certain conditions, they show that: (1) A compact set is stable if and only if its components are stable; (2) A compact set is asymptotically stable if and only if it has a finite number of components, each of which is asymptotically stable. Moreover, they characterize the stability of a compact set by means of \(\omega\)-limit sets, prolongations, prolongational limit sets and the existence of a fundamental system of neighborhoods of it. Finally, they present some applications to continuous flows and affine control systems.
reviewed by: Nilson C. jun. Bernardes
Mathematics Subject Classification ID: 37B25
Mathematics Subject Classification ID: 37C75
Mathematics Subject Classification ID: 37C85
Mathematics Subject Classification ID: 16W22
zbMATH DE Number: 7318666
zbMATH Keywords: Lyapunov stability
zbMATH Keywords: asymptotical stability
zbMATH Keywords: connected components
zbMATH Keywords: prolongations
zbMATH Keywords: semigroup actions
MaRDI profile type: Publication
full work available at URL: j.topol.2021.107611
OpenAlex ID: W3121159540
cites work: A characterization of completely regular spaces
cites work: Prolongations and stability in dynamical systems
cites work: Topological dynamics of control systems: Stability and attraction
cites work: Dynamical systems: Stability theory and applications
cites work: Q5614853
cites work: Attraction and Lyapunov stability for control systems on vector bundles
cites work: Attractors and chain recurrence for semigroup actions
cites work: Lyapunov stability for semigroup actions
cites work: Lyapunov Stability and Attraction Under Equivariant Maps
cites work: On attractors and stability for semigroup actions and control systems
cites work: Q3160248
cites work: Q5749640
cites work: Q4485837
cites work: Semiflows on topological spaces: chain transitivity and semigroups
cites work: Some aspects of stability for semigroup actions and control systems
cites work: Lyapunov functions and stability of dynamical polysystems
cites work: Q4820394
DOI: 10.1016/J.TOPOL.2021.107611
description: scientific article; zbMATH DE number 7318666