Bounded decomposition in the Brieskorn lattice and Pfaffian Picard--Fuchs systems for Abelian integrals

Details Bounded decomposition in the Brieskorn lattice and Pfaffian Picard--Fuchs systems for Abelian integrals Bounded decomposition in the Brieskorn lattice and Pfaffian Picard--Fuchs systems for Abelian integrals

2002-01-14

arxiv.org/abs/math/0201114v1

Bull. Sci. Math\'ematiques 126 (2002), issue 7, 535-554

Mathematics

Dynamical Systems

17 pages in LaTeX2e

Scientific paper

10.1016/S0007-4497(02)01126-0

We suggest an algorithm for derivation of the Picard--Fuchs system of Pfaffian equations for Abelian integrals corresponding to semiquasihomogeneous Hamiltonians. It is based on an effective decomposition of polynomial forms in the Brieskorn lattice. The construction allows for an explicit upper bound on the norms of the polynomial coefficients, an important ingredient in studying zeros of these integrals.

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