Global phase portraits of some reversible cubic centers with collinear or infinitely many singularities
Caubergh, Magdalena (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Torregrosa, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)

Date:	2012
Abstract:	We study the reversible cubic vector fields of the form ˙x = −y + ax2 + bxy + cy2 − y(x2 + y2), y˙ = x + dx2 + exy + fy2 + x(x2 + y2), having simultaneously a center at infinity and at the origin. In this paper the subclass of these reversible systems having collinear or infinitely many singularities are classified with respect to topological and diffeomorphic equivalence.
Grants:	Ministerio de Economía y Competitividad MTM2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2009/SGR-410
Note:	Agraïments: Furthermore the first author also is supported by the Juan de la Cierva grant number JCI-2007-49-764 and the second author also is partially supported by ICREA Academia.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Center-focus problem ; Reversible planar vector fields ; Cubic vector fields ; Global classification of phase portraits
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 22 Núm. 11 (2012) , p. 1250273 (20 pages), ISSN 1793-6551

DOI: 10.1142/S0218127412502732

Postprint 23 p, 2.0 MB

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