Quadratic Differential Systems with a Finite Saddle-Node and an Infinite Saddle-Node (1,1) SN - (A)
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)

Date:	2021
Abstract:	Our goal is to make 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 and infinite singularities. This class can be divided into two different families, being (A) possessing the finite saddle-node as the only finite singularity and (B) possessing the finite saddle-node and also a finite simple elemental singularity. In this paper we provide the complete study of the geometry of family (A). The family (A) modulo the action of the affine group and time homotheties are four-dimensional and we give the bifurcation diagram of its closure with respect to a specific normal form, in the four-dimensional real projective space Rℙ4. As far as we know, this is the first time that a complete family is studied in the four-dimensional real projective space. The respective bifurcation diagram yields 36 topologically distinct phase portraits for systems in the closure QsnSN11(A)¯ within the representatives of QsnSN11(A) given by a specific normal form.
Grants:	Agencia Estatal de Investigación MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617
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Language:	Anglès
Document:	Article ; recerca ; Versió acceptada per publicar
Subject:	Quadratic differential system ; Finite saddle-node ; Infinite saddle-node ; Phase portrait ; Bifurcation diagram ; Algebraic invariant
Published in:	International journal of bifurcation and chaos in applied sciences and engineering, Vol. 31, Issue 2 (February 2021) , art. 2150026, ISSN 1793-6551

DOI: 10.1142/S0218127421500267

Postprint 26 p, 518.0 KB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > GSD (Dynamical systems)
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