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

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

2005-07-11

arxiv.org/abs/math/0507213v1

Mathematics

Dynamical Systems

13 pages

Scientific paper

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.

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