Cubic systems with invariant affine straight lines of total parallel multiplicity seven

• Main Authors: Alexandru Suba, Vadim Repesco, Vitalie Putuntica
• Format: Article
• Language: English
• Published: Texas State University 2013-12-01
• Series: Electronic Journal of Differential Equations
• Subjects: Cubic differential system; invariant straight line; phase portrait
• Online Access: http://ejde.math.txstate.edu/Volumes/2013/274/abstr.html

In this article, we study the planar cubic differential systems with invariant affine straight lines of total parallel multiplicity seven. We classify these system according to their geometric properties encoded in the configurations of invariant straight lines. We show that there are only 17 different topological phase portraits in the Poincar\'e disc associated to this family of cubic systems up to a reversal of the sense of their orbits, and we provide representatives of every class modulo an affine change of variables and rescaling of the time variable.