Quadratic systems with an integrable saddle: A complete classification in the coefficient space R^12
Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)

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

DOI: 10.1016/j.na.2012.04.043

Postprint 38 p, 831.0 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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