English

Higher order Poincare-Pontryagin functions and iterated path integrals

Dynamical Systems 2007-05-23 v2

Abstract

We prove that the higher order Poincare-Pontryagin functions associated to the perturbed polynomial foliation dfϵ(Pdx+Qdy)=0df -\epsilon (P dx + Q dy) =0 satisfy a differential equation of Fuchs type.

Cite

@article{arxiv.math/0403284,
  title  = {Higher order Poincare-Pontryagin functions and iterated path integrals},
  author = {Lubomir Gavrilov},
  journal= {arXiv preprint arXiv:math/0403284},
  year   = {2007}
}

Comments

This is a revised version containing the following changes: reference [18] is added, some notations are changed, the proof of Theorem 1 is corrected, Theorem B1 and B2 are replaced now by Theorem B, some signs are corrected in the Appendix. The paper will appear in "Annales de la Faculte des Sciences de Toulouse", 2005

R2 v1 2026-07-22T17:03:28.570Z