Global configurations of singularities for quadratic differential systems with exactly three finite singularities of total multiplicity four
Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Schlomiuk, Dana (Université de Montréal. Département de Mathématiques et de Statistiques)
Vulpe, Nicolae (Academy of Science of Moldova)

Data:	2015
Resum:	In this article we obtain the geometric classification of singularities, finite and infinite, for the two subclasses of quadratic differential systems with total finite multiplicity m_f=4 possessing exactly three finite singularities, namely: systems with one double real and two complex simple singularities (31 configurations) and (ii) systems with one double real and two simple real singularities (265 configurations). We also give here the global bifurcation diagrams of configurations of singularities, both finite and infinite, with respect to the geometric equivalence relation, for these classes of quadratic systems. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of polynomial invariants. This gives an algorithm for determining the geometric configuration of singularities for any system in anyone of the two subclasses considered.
Ajuts:	Ministerio de Economía y Competitividad MTM2008-03437 Ministerio de Economía y Competitividad UNAB13-4E-1604 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 European Commission 316338
Nota:	Agraïments: The third author is supported by NSERC Grant RN000355. The fourth author is partially supported NSERC Grant RN000355.
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Affine invariant polynomials ; Configuration of singularities ; Geometric equivalence relation ; Infinite and finite singularities ; Poincaré compactification ; Quadratic vector fields
Publicat a:	Electronic Journal of Qualitative Theory of Differential Equations, Vol. 49 (2015) , p. 1-60, ISSN 1417-3875

DOI: 10.14232/ejqtde.2015.1.49
DOI: 10.14232/ejqtde.2015.1.49

Postprint 60 p, 2.7 MB

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