Ramazi Pouria; Cao Ming; Scherpen Jacquelien M. A.: Tightening Poincaré-Bendixson theory after counting separately the fixed points on the boundary and interior of a planar region. (2024)
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This paper tightens the classical Poincaré–Bendixson theory for a positively invariant, simply-connected compact set M in a continuously differentiable planar vector field by further characterizing for any point p ∈ M, the composition of the limit sets ω(p) and α(p) after counting separately the fixed points on M’s boundary and interior. In particular, when M contains finitely many boundary but no interior fixed points, ω(p) contains only a single fixed point, and when M may have infinitely many boundary but no interior fixed points, ω(p) can, in addition, be a continuum of fixed points. When M contains only one interior and finitely many boundary fixed points, ω(p) or α(p) contains exclusively a fixed point, a closed orbit or the union of the interior fixed point and homoclinic orbits joining it to itself. When M contains in general a finite number of fixed points and neither ω(p) nor α(p) is a closed orbit or contains just a fixed point, at least one of ω(p) and α(p) excludes all boundary fixed points and consists only of a number of the interior fixed points and orbits connecting them.
| Mű típusa: | Folyóirat |
|---|---|
| Folyóirat/könyv/kiadvány címe: | Electronic journal of qualitative theory of differential equations |
| Dátum: | 2024 |
| Szám: | 29 |
| ISSN: | 1417-3875 |
| Oldalszám: | 9 |
| Nyelv: | angol |
| Kiadás helye: | Szeged |
| DOI: | 10.14232/ejqtde.2024.1.29 |
| Kulcsszavak: | Poincaré-Bendixson-elmélet, Dinamikai rendszer, Differenciálegyenlet |
| Megjegyzések: | Bibliogr.: p. 8-9. ; összefoglalás angol nyelven |
| Szakterület: | 01. Természettudományok 01. Természettudományok > 01.01. Matematika |
| Feltöltés dátuma: | 2025. nov. 17. 12:29 |
| Utolsó módosítás: | 2025. nov. 17. 12:38 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/88831 |
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