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Structurally unstable quadratic vector fields of codimension one

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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  Read more...

Abstract: 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

Author(s): Artés, Joan C.; Llibre, Jaume; Rezende, Alex C
Publisher: Springer International Publishing : Imprint: Birkhäuser
Year: 2018

Language: English
Pages: 267
Tags: Mathematics.;Dynamics.;Ergodic theory.;Differential equations.;Mathematics -- Mathematical Analysis.;Nonlinear science.;Mathematics -- Differential Equations.;Differential calculus & equations.;Ordinary Differential Equations.;Dynamical Systems and Ergodic Theory.

Content: 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.