Home > Articles > Published articles > Quadratic systems with an integrable saddle: A complete classification in the coefficient space R^12 |
Date: | 2012 |
Abstract: | A quadratic polynomial differential system can be identified with a single point of R12 through the coefficients. Using the algebraic invariant theory we classify all the quadratic polynomial differential systems of R12 having an integrable saddle. We show that there are only 47 topologically different phase portraits in the Poincar'e disc associated to this family of quadratic systems up to a reversal of the sense of their orbits. Moreover each one of these 47 representatives is determined by a set of affine invariant conditions. |
Grants: | Ministerio de Ciencia e Innovación MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Quadratic vector fields ; Weak saddle ; Type of singularity |
Published in: | Nonlinear Analysis : Theory, Methods and Applications, Vol. 75 (2012) , p. 5416-5447, ISSN 0362-546X |
Postprint 38 p, 831.0 KB |