Quadratic systems with an invariant conic having Darboux invariants
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Oliveira, Regilene (Universidade de Sâo Paulo (Brazil). Departamento de Matemática)

Date:	2018
Abstract:	The complete characterization of the phase portraits of real planar quadratic vector fields is very far to be completed. As this attempt is not possible in the whole class due to the large number of parameters (twelve, but, after affine transformations and time rescaling, we arrive at families with five parameters, which is still a big number of parameters), many subclasses have been considered and studied. In this paper we complete the characterization of the global phase portraits in the Poincaré disc of all planar quadratic polynomial differential systems having an invariant conic and a Darboux invariant, constructed using only the invariant conic.
Rights:	Tots els drets reservats.
Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Darboux invariant ; Phase portraits ; Quadratic vector fields
Published in:	Communications in contemporaray mathematics, Vol. 20, issue 4 (2018) , art. 1750033, ISSN 1793-6683

DOI: 10.1142/S021919971750033X

Postprint 15 p, 365.0 KB

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