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.
Author(s): Bernard Candelpergher, Francine Diener, Marc Diener (auth.), Jean-Pierre Françoise, Robert Roussarie (eds.)
Series: Lecture Notes in Mathematics 1455
Edition: 1
Publisher: Springer Berlin Heidelberg
Year: 1990
Language: English-French
Pages: VIII, 400 p.
City: Berlin; New York
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
