Structurally Unstable Quadratic Vector Fields of Codimension One

Originating from research in the qualitative theory of ordinary differential equations, this book follows the authors' work on structurally stable planar quadratic polynomial differential systems. In the present work the authors aim at finding all possible phase portraits in the Poincaré disc, modulo limit cycles, of planar quadratic polynomial differential systems manifesting the simplest level of structural instability. They prove that there are at most 211 and at least 204 of them.

Follows a similar work on structurally stable systems Proves that there are at most 211 and at least 204 structurally unstable codimension one topologically different phase portraits in the Poincaré disc modulo limit cycles Gives an overview on recent research in the area

Inhalt
Introduction.- Preliminary definitions.- Some preliminary tools.- A summary for the structurally stable quadratic vector fields.- Proof of Theorem 1.1(a).- Proof of Theorem 1.1(b).- Bibliography.