Quartic differential systems with a non-degenerate monodromic critical point and multiple line at infinity

Abstract

The quartic differential systems with a non-degenerate monodromic critical point and non-degenerate infinity are considerated. We show that in this family the maximal multiplicity of the line at infinity is seven. Modulo the affine transformation and time rescaling the classes of systems with the line of infinity of multiplicity two, three, ..., seven are determinated. In the cases when the quartic systems have the line at infinity of maximal multiplicity the problem of the center is solved.