English

Contour integrals as $Ad$-invariant functions on the fundamental group

Dynamical Systems 2007-05-23 v1 Complex Variables

Abstract

We introduce a general approach to contour integrals. It covers usual Abelian integrals, the higher order Melnikov integrals and the generalized Abelian integrals. We prove that the generating function always satisfies a linear differential equation of finite order. We also present a relationship between the generalized Abelian integral and certain representation of the fundamental group of complex curve.

Keywords

Cite

@article{arxiv.math/0507213,
  title  = {Contour integrals as $Ad$-invariant functions on the fundamental group},
  author = {Marcin Bobienski},
  journal= {arXiv preprint arXiv:math/0507213},
  year   = {2007}
}

Comments

13 pages

R2 v1 2026-07-22T17:21:56.190Z