Home > Articles > Published articles > Planar vector fields with a given set of orbits |
Date: | 2011 |
Abstract: | We determine all the C 1 planar vector fields with a given set of orbits of the form y − y(x) = 0 satisfying convenient assumptions. The case when these orbits are branches of an algebraic curve is also study. We show that if a quadratic vector field admits a unique irreducible invariant algebraic curve g(x, y) = S∑j=0 aj (x)y S−j = 0 with S branches with respect to the variable y, then the degree of the polynomial g is at most 4S. |
Grants: | Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 Ministerio de Economía y Competitividad DPI2007-66556-C03-03 Ministerio de Economía y Competitividad TSI2007-65406-C03-01 Ministerio de Economía y Competitividad CSD2007-00004 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Invariant curve ; Singular algebraic curve ; Branches ; Quadratic vector fields ; Orthogonal polynomial ; Orbits |
Published in: | Journal of dynamics and differential equations, Vol. 23 Núm. 4 (2011) , p. 885-902, ISSN 1572-9222 |
Postprint 20 p, 347.7 KB |