Structurally Unstable Quadratic Vector Fields of Codimension One [electronic resource] /
Artés, Joan C.author.
Llibre, Jaume.author.
Rezende, Alex C.author.
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. .
Includes bibliographical references.
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.
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. .
Differential equations.
Dynamics.
Ergodic theory.
Ordinary Differential Equations.
Dynamical Systems and Ergodic Theory.