Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1, 1) SN-(B)
Artés Ferragud, Joan Carles (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Mota, Marcos C. (Universidade de São Paulo. Instituto de Ciências Matemáticas e de Computação)
Rezende, Alex C. (Universidade Federal de São Carlos. Departamento de Matemática)

Data:	2021
Resum:	This paper presents a global study of the class QsnSN11 of all real quadratic polynomial differential systems which have a finite semi-elemental saddle-node and an infinite saddle-node formed by the coalescence of a finite singularity and an infinite singularity. This class can be divided into two different families, namely, QsnSN11(A) phase portraits possessing a finite saddle-node as the only finite singularity and QsnSN11(B) phase portraits possessing a finite saddle-node and also a simple finite elemental singularity. Each one of these two families is given by a specific normal form. The study of family QsnSN11(A) was reported in [Artés et al. , 2020b] where the authors obtained 36 topologically distinct phase portraits for systems in the closure QsnSN11(A)¯. In this paper, we provide the complete study of the geometry of family QsnSN11(B). This family which modulo the action of the affine group and time homotheties is three-dimensional and we give the bifurcation diagram of its closure with respect to a specific normal form, in the three-dimensional real projective space. The respective bifurcation diagram yields 631 subsets with 226 topologically distinct phase portraits for systems in the closure QsnSN11(B)¯ within the representatives of QsnSN11(B) given by a specific normal form. Some of these phase portraits are proven to have at least three limit cycles.
Ajuts:	Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
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Llengua:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Matèria:	Quadratic differential system ; Finite saddle-node ; Finite elemental singularity ; Infinite saddle-node ; Phase portrait ; Bifurcation diagram ; Algebraic invariant
Publicat a:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 31, Issue 9 (July 2021) , art. 2130026, ISSN 1793-6551

DOI: 10.1142/S0218127421300263

Postprint 126 p, 2.9 MB

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