Geometry of planar quadratic systems
| dc.creator | Gaiko, Valery A. | |
| dc.date | 2006-11-06 | |
| dc.date.accessioned | 2026-07-07T07:32:34Z | |
| dc.date.available | 2026-07-07T07:32:34Z | |
| dc.description | In this paper, the global qualitative analysis of planar quadratic dynamical systems is established and a new geometric approach to solving Hilbert's Sixteenth Problem in this special case of polynomial systems is suggested. Using geometric properties of four field rotation parameters of a new canonical system which is constructed in this paper, we present a proof of our earlier conjecture that the maximum number of limit cycles in a quadratic system is equal to four and the only possible their distribution is (3:1). Besides, applying the Wintner-Perko termination principle for multiple limit cycles to our canonical system, we prove in a different way that a quadratic system has at most three limit cycles around a singular point (focus) and give another proof of the same conjecture. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0611142 | |
| dc.identifier | http://arxiv.org/abs/math/0611142 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/119156 | |
| dc.subject | Dynamical Systems | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 34C05, 34C07, 34C23, 37G05, 37G10, 37G15 | |
| dc.title | Geometry of planar quadratic systems | |
| dc.type | text |