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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75745We 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.13 pagesDynamical SystemsComplex Variables34C07,34C08Contour integrals as $Ad$-invariant functions on the fundamental grouptext