Canonical forms for cubic differential systems with affine real invariant straight lines of total parallel multiplicity six and configurations (2(m), 2(n), 1, 1)

Abstract

The classification of all cubic systems with the maximum number of invariant straight lines, including the line at infinity, and taking into account their geometric multiplicities, is given in [1], [4], [5]. The cubic systems with exactly eight and exactly seven distinct affine invariant straight lines have been studied in [4], [5]; with invariant straight lines of total geometric (parallel) multiplicity eight (seven) - in [2], [3], [8], and with six real invariant straight lines along two (three) directions – in [6], [7]. In [9] it was shown that in the class of cubic differential systems the maximal multiplicity of an affine real straight line is seven. In this paper are obtained canonical forms for cubic differential systems with affine real invariant straight lines of total parallel multiplicity six and configurations (2(m), 2(n), 1, 1).