Cristina Bujac, Dana Schlomiuk, Nicolae Vulpe
Abstract:
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
Show me the PDF file (2046 KB), TEX file for this article.
 |
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 |
Return to the EJDE web page