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

DOI10.1016/S0007-4497(02)01126-0zbMath1021.34026arXivmath/0201114OpenAlexW3216983926MaRDI QIDQ1865009

Sergey Yu. Yakovenko

Publication date: 23 March 2003

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0201114

zbMATH Keywords

Picard-Fuchs equationsBrieskorn latticerelative homologyAbelian integrals

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Global theory of complex singularities; cohomological properties (32S20) Monodromy; relations with differential equations and (D)-modules (complex-analytic aspects) (32S40) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50)

Related Items (6)

Linear estimate for the number of zeros of abelian integrals ⋮ On the number of zeros of Abelian integrals for a polynomial Hamiltonian irregular at infinity ⋮ Perturbations of non-Hamiltonian reversible quadratic systems with cubic orbits ⋮ Picard-Fuchs equations and Gauss-Manin systems with a view towards the Riemann-Hilbert problem ⋮ On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem ⋮ Singularities of functions on the Martinet plane, constrained Hamiltonian systems and singular Lagrangians

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