Structurally Unstable Quadratic Vector Fields of Codimension One

Description

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. Front Matter ....Pages i-vi Introduction (Joan C. Artés, Jaume Llibre, Alex C. Rezende)....Pages 1-19 Preliminary Definitions (Joan C. Artés, Jaume Llibre, Alex C. Rezende)....Pages 21-28 Some Preliminary Tools (Joan C. Artés, Jaume Llibre, Alex C. Rezende)....Pages 29-50 A Summary of Structurally Stable Quadratic Vector Fields (Joan C. Artés, Jaume Llibre, Alex C. Rezende)....Pages 51-58 Proof of Theorem 1.1(a) (Joan C. Artés, Jaume Llibre, Alex C. Rezende)....Pages 59-184 Proof of Theorem 1.1(b) (Joan C. Artés, Jaume Llibre, Alex C. Rezende)....Pages 185-264 Back Matter ....Pages 265-267