The family of cubic differential systems with two real and two complex distinct infinite singularities and invariant straight lines of the type <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns="http://www.w3.org/1998/Math/MathML"> <mml:mo stretchy="false">(</mml:mo> <mml:mn>3</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo>,</mml:mo> <mml:mn>1</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math>-Reference-Cited by-同舟云学术

The family of cubic differential systems with two real and two complex distinct infinite singularities and invariant straight lines of the type ( 3 , 1 , 1 , 1 )

Published:2023 Issue:40 Volume: Page:1-94
ISSN:1417-3875
Container-title:Electronic Journal of Qualitative Theory of Differential Equations
language:en
Short-container-title:Electron. J. Qual. Theory Differ. Equ.

Author:

Bujac Cristina¹,Schlomiuk Dana²,Vulpe Nicolae¹

Affiliation:

1. State University of Moldova

2. Université de Montréal

Abstract

In this article we consider the class CSL 7 2 r 2 c ∞ of non-degenerate real planar cubic vector fields, which possess two real and two complex distinct infinite singularities and invariant straight lines of total multiplicity 7, including the line at infinity. The classification according to the configurations of invariant lines of systems possessing invariant straight lines was given in articles published from 2014 up to 2022. We continue our investigation for the family CSL 7 2 r 2 c ∞ possessing configurations of invariant lines of type ( 3 , 1 , 1 , 1 ) and prove that there are exactly 42 distinct configurations of this type. Moreover we construct all the orbit representatives of the systems in this class with respect to affine group of transformations and a time rescaling.

Funder

NSERC

Publisher

University of Szeged

Subject

Applied Mathematics

Link

http://www.math.u-szeged.hu/ejqtde/p10272.pdf

Reference47 articles.

1. On the number of invariant straight lines for polynomial differential systems

2. V. A. Baltag, Algebraic equations with invariant coefficients in qualitative study of the polynomial homogeneous differential systems, Bul. Acad. Stiin te Repub. Mold. Mat. 42(2003), No. 2, 13--27.

3. V. A. Baltag, N. I. Vulpe, Total multiplicity of all finite critical points of the polynomial differential system, Planar nonlinear dynamical systems (Delft, 1995), Differ. Equ. Dyn. Syst. 5(1997), no. 3--4, 455--471.

4. C. Bujac, One new class of cubic systems with maximum number of invariant lines omitted in the classification of J. Llibre and N. Vulpe, Bul. Acad. Stiinte Repub. Mold., Mat. 75(2014), No. 2, 102--105.

5. C. Bujac, One subfamily of cubic systems with invariant lines of total multiplicity eight and with two distinct real infinite singularities, Bul. Acad. Stiinte Repub. Mold., Mat. (2015), No. 1(77), 48--86.