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

Bernard Candelpergher, Francine Diener, Marc Diener (auth.), Jean-Pierre Françoise, Robert Roussarie (eds.)3540535098, 9783540535096, 0387535098

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.

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Table of contents :

Content:
Front Matter….Pages –
Retard � la bifurcation : du local au global….Pages 1-19
On bifurcation of limit cycles from centers….Pages 20-43
On the saddle loop bifurcation….Pages 44-73
Finitude des cycles-limites et accelero-sommation de l’application de retour….Pages 74-159
Limit cycles and zeroes of Abelian integrals satisfying third order picard — Fuchs equations….Pages 160-186
On the basin of attraction of dissipative planar vector fields….Pages 187-195
Periodic lines of curvature bifurcating from Darbouxian umbilical connections….Pages 196-229
Conditions for a centre and the bifurcation of limit cycles in a class of cubic systems….Pages 230-242
On first integrals of linear systems, Frobenius integrability theorem and linear representations of Lie algebras….Pages 243-271
Cyclicite finie des polycycles hyperboliques de champs de vecteurs du plan mise sous forme normale….Pages 272-314
Bifurcation of limit cycles….Pages 315-333
Universal unfolding of a singularity of a symmetric vector field with 7-jet C∞-equivalent to y ∂/∂x+(±x3 ±x6y) ∂/∂y….Pages 334-355
Bifurcation in a quartic polynomial system arising in biology….Pages 356-368
On the finiteness of certain boundary cycles for NTH degree polynomial vector fields….Pages 369-372
Algebraic integrals of quadratic systems with a weak focus….Pages 373-384
Rotated vector fields decomposition method and its application….Pages 385-392
Remarks on the delay of the loss of stability of systems with changing parameter….Pages 393-396