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

Autor(es)

Artes, Joan C. ^[1] ; Mota, Marcos C. ^[2] ; Rezende, Alex C. ^[3]

Afiliação do(s) autor(es)

^[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13566590 Sao Paulo, SP - Brazil

^[3] Univ Fed Sao Carlos, Dept Matemat, BR-13565905 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS; v. 31, n. 2 FEB 2021.
• Citações Web of Science: 0

Resumo

Our goal is to make a global study of the class <mml:mstyle mathvariant={''}bold{''}>QsnSN11</mml:mstyle> 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 P4. 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 <mml:mstyle mathvariant={''}bold{''}>QsnSN11(A)</mml:mstyle><overbar></mml:mover> within the representatives of <mml:mstyle mathvariant={''}bold{''}>QsnSN11(A<mml:mo class={''}MathClass-close{''} stretchy={''}false{''}>)</mml:mstyle> given by a specific normal form. (AU)

• Processo FAPESP: 18/21320-7 - Investigação de sistemas diferenciais quadráticos planares de codimensão dois
• Beneficiário: Alex Carlucci Rezende
• Modalidade de apoio: Bolsas no Exterior - Pesquisa