\(B\)-stability and the Florio-Seibert problem (Q2704018)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: \(B\)-stability and the Florio-Seibert problem |
scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | \(B\)-stability and the Florio-Seibert problem |
scientific article |
Statements
20 January 2002
0 references
stability
0 references
semiasymptotic stability
0 references
asymptotic stability
0 references
global stability
0 references
\(B\)-stability
0 references
sets of the type \((B)\)
0 references
first prolongation
0 references
first prolongational limit set
0 references
\(B\)-stability and the Florio-Seibert problem (English)
0 references
The author discusses stability-type properties of sets in dynamical systems on metric space. The notion of the \(B\)-stability (introduced and discussed previously in the author's papers [Differ. Uravn. 25, No. 4, 727-729 (1989; Zbl 0683.54042) and ibid. 27, No. 5, 758-766 (1991; Zbl 0745.34050)]) is characterized by certain necessary and sufficient conditions described in the theorems 1 and 2. Sets of the type \((B)\) are defined and characterized by theorems 3-7. The Florio-Seibert problem concerning conditions sufficient for stability, asymptotic stability and global asymptotic stability of compact sets is discussed in the last part of the paper; the theorems 8-10 give some answers to that problem.
0 references
