Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan. Algorithme de finitude. (Finite cyclicity of hyperbolic polycycles of plane vector fields. Finiteness algorithm). (French) Zbl 0725.58032

Mourtada, Abderaouf

Ann. Inst. Fourier 41, No. 3, 719-753 (1991).

We show that generic hyperbolic polycycles are of finite cyclicity in smooth families of vector fields on the plane. A consequence is that the Hilbert 16th problem is locally true in some open dense subset of the space of polynomial vector fields on the plane of degree less than or equal to n.

Reviewer: A.Mourtada (Dijon)

MSC:

37D99

Dynamical systems with hyperbolic behavior

Keywords:

saddle point; generic unfolding; hyperbolicity ratio; displacement map; finite cyclicity; vector fields