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The classification of a family of cubic differential systems in terms of configurations of invariant lines of the type $(3,3)$

Cristina Bujac

Vladimir Andrunachievici Institute of Mathematics and Computer Science

Abstract: In this article we consider the class of non-degenerate real planar cubic vector fields, which possess two real and two complex distinct infinite singularities and invariant straight lines, including the line at infinity, of total multiplicity $7$. In addition, the systems from this class possess configurations of the type $(3,3)$. We prove that there are exactly $16$ distinct configurations of invariant straight lines for this class and present corresponding examples for the realization of each one of the detected configurations.

Keywords and phrases: cubic differential system, invariant straight line, multiplicity of invariant lines, infinite and finite singularities, affine invariant polynomial, group action, configuration of invariant lines, multiplicity of singularity.

MSC: 58K45, 34C05, 34A34

Received: 10.08.2019

Language: English