Abelian integrals in holomorphic foliations.

DOI10.4171/RMI/385zbMath1055.37057arXivmath/0203062MaRDI QIDQ1880522

Hossein Movasati

Publication date: 28 September 2004

Published in: Revista Matemática Iberoamericana (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0203062

zbMATH Keywords

limit cyclesHilbert's 16th problemPicard-Lefschetz theoryalgebro-geometric approach

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) 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) Dynamical aspects of holomorphic foliations and vector fields (37F75)

Related Items (9)

Mixed Hodge structure of affine hypersurfaces ⋮ Meromorphic connections on \(\mathbb P^1\) and the multiplicity of Abelian integrals ⋮ The Poincaré center problem ⋮ Analytic deformations of pencils and integrable one-forms having a first integral ⋮ Center conditions: Rigidity of logarithmic differential equations. ⋮ Brieskorn module and center conditions: pull-back of differential equations in projective space ⋮ The monodromy problem for hyperelliptic curves ⋮ On elliptic modular foliations ⋮ Center conditions: Pull-back of differential equations

Cites Work

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• Integrals for holomorphic foliations with singularities having all leaves compact
• Petrov modules and zeros of abelian integrals
• Relative cohomology of polynomial mappings
• Irreducible components of the space of holomorphic foliations of degree two in \(\mathbb{C} P(n)\), \(n\geq 3\)
• Monodromy of isolated singularities of hypersurfaces
• Successive derivatives of a first return map, application to the study of quadratic vector fields
• Vanishing Cycles in a Pencil of Hyperplane Sections of a Non-Singular Quasi-Projective Variety

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