First integrals and phase portraits of planar polynomial differential cubic systems with the maximum number of invariant straight lines
Bujac, Cristina (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Vulpe, Nicolae (Academy of Sciences of Moldova. Institute of Mathematics and Computer Science)

Data:	2016
Resum:	In the article LliVul2006 the family of cubic polynomial differential systems possessing invariant straight lines of total multiplicity 9 was considered and 23 such classes of systems were detected. We recall that 9 invariant straight lines taking into account their multiplicities is the maximum number of straight lines that a cubic polynomial differential systems can have if this number is finite. Here we complete the classification given in LliVul2006 by adding a new class of such cubic systems and for each one of these 24 such classes we perform the corresponding first integral as well as its phase portrait. Moreover we present necessary and sufficient affine invariant conditions for the realization of each one of the detected classes of cubic systems with maximum number of invariant straight lines when this number is finite.
Ajuts:	European Commission 316338 European Commission 318999 Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568
Drets:	Tots els drets reservats.
Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Publicat a:	Qualitative theory of dynamical systems, Vol. 15 (2016) , p. 327-348, ISSN 1662-3592

DOI: 10.1007/s12346-016-0211-2

Postprint 22 p, 1.1 MB

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