Phase portraits of planar semi-homogeneous vector fields. II (Q1961266)

The authors study phase-portraits of semi-homogeneous plane vector fields of degrees \(1\) and \(3\), \[ \dot x= ax+ by,\quad \dot y= Ax^3+ Bx^2y+ Cxy^2+ Dy^3,\tag{1} \] with \(|a|+|b|\neq 0\) and \(|A|+|B|+|C|+|D|\neq 0\), and having only finitely many critical points. They prove that topologically there are 32 different configurations modulus limit cycles; among which 13 have a focus or a node, perhaps surrounded by limit cycles; \(4\) have a focus or a node surrounded by at least one limit cycle; one has a center: \(14\) have a saddle point. They give also canonical forms of (1) having these configurations. The details of all calculations are not included. [For part I see Zbl 0886.34026].