Bifurcations of Planar Vector Fields: Proceedings of a Meeting Held in Luminy, France, Sept. 18-22, 1989

ISBN-13: 9783540535096 / Angielski / Miękka / 1990 / 400 str.

Jean-Pierre Francoise; Robert Roussarie

Opis

A collection of papers on differential equations and dynamical systems which stresses topics relating to Hilbert's 16th problem. Among these are a solution to Dulac's problem, results on the multiplicity of singular cycles and results on the zeroes of abelian integrals.

Spis treści

Retard à la bifurcation : du local au global.- On bifurcation of limit cycles from centers.- On the saddle loop bifurcation.- Finitude des cycles-limites et accelero-sommation de l’application de retour.- Limit cycles and zeroes of Abelian integrals satisfying third order picard — Fuchs equations.- On the basin of attraction of dissipative planar vector fields.- Periodic lines of curvature bifurcating from Darbouxian umbilical connections.- Conditions for a centre and the bifurcation of limit cycles in a class of cubic systems.- On first integrals of linear systems, Frobenius integrability theorem and linear representations of Lie algebras.- Cyclicite finie des polycycles hyperboliques de champs de vecteurs du plan mise sous forme normale.- Bifurcation of limit cycles.- Universal unfolding of a singularity of a symmetric vector field with 7-jet C?-equivalent to y ?/?x+(±x3 ±x6y) ?/?y.- Bifurcation in a quartic polynomial system arising in biology.- On the finiteness of certain boundary cycles for NTH degree polynomial vector fields.- Algebraic integrals of quadratic systems with a weak focus.- Rotated vector fields decomposition method and its application.- Remarks on the delay of the loss of stability of systems with changing parameter.