The infinitesimal 16th Hilbert problem in dimension zero

DOI10.1016/j.bulsci.2006.04.003zbMath1119.14040arXivmath/0507061OpenAlexW2143458681MaRDI QIDQ877900

Hossein Movasati, Lyubomir Gavrilov

Publication date: 4 May 2007

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

Full work available at URL: https://arxiv.org/abs/math/0507061

zbMATH Keywords

infinitesimal 16th Hilbert problemabelian integral

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) Structure of families (Picard-Lefschetz, monodromy, etc.) (14D05) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Singularities of holomorphic vector fields and foliations (32S65) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items

Infinitesimal center problem on zero cycles and the composition conjecture, On the trigonometric moment problem, The monodromy problem and the tangential center problem, On the center-focus problem for the equation \(\frac{\mathrm{d}y}{\mathrm{d}x} + \Sigma_{i=1}^n a_i(x) y^i = 0\), \(0\leq x \leq 1\) where \(a_i\) are polynomials, The monodromy problem for hyperelliptic curves, On elliptic modular foliations

Uses Software

• foliation.lib

Cites Work

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