This book deals with systems of polynomial autonomous ordinary differential equations in two real variables. The emphasis is mainly qualitative, although attention is also given to more algebraic aspects as a thorough study of the center/focus problem and recent results on integrability. In the last two chapters the performant software tool P4 is introduced. From the start, differential systems are represented by vector fields enabling, in full strength, a dynamical systems approach. All essential notions, including invariant manifolds, normal forms, desingularization of singularities, index theory and limit cycles, are introduced and the main results are proved for smooth systems with the necessary specifications for analytic and polynomial systems.This can be obtained by using the so called Newton diagram. We first define the Newton diagram. Let X = P(x, y)aax + Q(x, y)aay be a polynomial vector field with an isolated singularity at the origin. a Let P(x, y) = aijxiyj and Q(x, y) = bijxiyj.
|Title||:||Qualitative Theory of Planar Differential Systems|
|Author||:||Freddy Dumortier, Jaume Llibre, Joan C. Artés|
|Publisher||:||Springer Science & Business Media - 2006-10-13|