DARBOUX INTEGRABLE SYSTEM WITH A TRIPLE POINT AND PSEUDO-ABELIAN INTEGRALS

Aymen Braghtha (1)

1 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We study pseudo-abelian integrals associated with polynomial perturbations of Darboux integrable system with a triple point. Under some assumptions we prove the local boundedness of the number of their zeros. Assuming that this is the only non-genericity, we prove that the number of zeros of the corresponding pseudo-abelian integrals is bounded uniformly for nearby Darboux integrable foliations.

Mots clés: Abelian integrals; Limit Cycle; Darboux integrability

Domaines: Systèmes dynamiques [math.DS]

Aymen Braghtha. DARBOUX INTEGRABLE SYSTEM WITH A TRIPLE POINT AND PSEUDO-ABELIAN INTEGRALS. 2016. ⟨hal-01388054v2⟩