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.
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