Electron. J. Differential Equations, Vol. 2021 (2021), No. 83, pp. 1-110.

Cubic differential systems with invariant straight lines of total multiplicity seven and four real distinct infinite singularities

Cristina Bujac, Dana Schlomiuk, Nicolae Vulpe

In this article we consider the class CSL74s∞ of non-degenerate real planar cubic vector fields possessing four distinct real infinite singularities and invariant straight lines, including the line at infinity of total multiplicity 7. We prove that there are exactly 93 distinct configurations of invariant straight lines for this class, and present corresponding examples for the realization of each one of the detected configurations.

Submitted December 21, 2018. Published October 3, 2021.
Math Subject Classifications: 58K45, 34C05, 34A34.
Key Words: Cubic vector field; invariant straight line; multiplicity of singularity; infinite and finite singularities; multiplicity of invariant lines; configurations of invariant straight lines.
DOI: https://doi.org/10.58997/ejde.2021.83

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Cristina Bujac
Vladimir Andrunachievici Institute of Mathematics and Computer Science
Chisnau, MD-2028, Moldova
email: crisulicica@yahoo.com
Dana Schlomiuk \newline Departement de Mathematiques et de Statistiques
Universite de Montreal, C.P. 6128
succursale Centre-Ville, Montreal
(Quebec) H3C 3J7, Canada
email: dana.schlomiuk@umontreal.ca
Nicolae Vulpe
Vladimir Andrunachievici Institute of Mathematics and Computer Science
Chisinau, MD-2028, Moldova
email: nvulpe@gmail.com

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