A polynomial vector field with singular points only of Poincaré type (Q1063740)

The basic result of the note is the following theorem. In the space of all polynomial vector fields of degree N on \({\mathbb{C}}^ n\) for any n and N there exists an open set which is formed of fields without singular points of Siegel type, and also an open set which is formed of fields without singular points of Poincaré type.