TY - JOUR

T1 - Global configurations of singularities for quadratic differential systems with exactly two finite singularities of total multiplicity four

AU - Artés, Joan C.

AU - Llibre, Jaume

AU - Rezende, Alex C.

AU - Schlomiuk, Dana

AU - Vulpe, Nicolae

PY - 2014/1/1

Y1 - 2014/1/1

N2 - © 2014, University of Szeged. All rights reserved. In this article we obtain the geometric classification of singularities, finite and infinite, for the three subclasses of quadratic differential systems with finite singularities with total multiplicity mf = 4 possessing exactly two finite singularities, namely: (i) systems with two double complex singularities (18 configurations); (ii) systems with two double real singularities (33 configurations) and (iii) systems with one triple and one simple real singularities (123 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 subclasses of systems. The bifurcation set of this diagram is algebraic. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of invariant polynomials, which give an algorithm for determining the geometric configuration of singularities for any quadratic system.

AB - © 2014, University of Szeged. All rights reserved. In this article we obtain the geometric classification of singularities, finite and infinite, for the three subclasses of quadratic differential systems with finite singularities with total multiplicity mf = 4 possessing exactly two finite singularities, namely: (i) systems with two double complex singularities (18 configurations); (ii) systems with two double real singularities (33 configurations) and (iii) systems with one triple and one simple real singularities (123 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 subclasses of systems. The bifurcation set of this diagram is algebraic. The bifurcation diagram is done in the 12-dimensional space of parameters and it is expressed in terms of invariant polynomials, which give an algorithm for determining the geometric configuration of singularities for any quadratic system.

KW - Affine invariant polynomials

KW - Configuration of singularities

KW - Geometric equivalence relation

KW - Infinite and finite singularities

KW - Poincaré compactification

KW - Quadratic vector fields

U2 - https://doi.org/10.14232/ejqtde.2014.1.60

DO - https://doi.org/10.14232/ejqtde.2014.1.60

M3 - Article

VL - 2014

SP - 1

EP - 43

JO - Electronic Journal of Qualitative Theory of Differential Equations

JF - Electronic Journal of Qualitative Theory of Differential Equations

SN - 1417-3875

ER -