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

2002/01/14 by S. Yakovenko, Sergei Yakovenko
Computer Science · Mathematics · #Advanced Combinatorial Mathematics #Advanced Differential Equations and Dynamical Systems #Polynomial and algebraic computation #math.AG #math.DS #msc:32S20 #msc:32S40 #msc:34C08 #msc:34M50

paper · pdf · doi:10.1016/s0007-4497(02)01126-0

published as Bull. Sci. Mathématiques 126 (2002), issue 7, 535-554 · 17 pages in LaTeX2e

arxiv created 2002/01/14 · openalex publication_date 2002/08/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Redundant Picard–Fuchs System for Abelian Integrals
• Calculation of mixed Hodge structures, Gauss-Manin connections and Picard-Fuchs equations
• Pseudo-Abelian integrals: unfolding generic exponential case
• Picard-Fuchs equations, Integrable Systems, and higher Algebraic K-theory
• The Pfaff lattice, Matrix integrals and a map from Toda to Pfaff