Affine upper bounds for the number of zeros of abelian integrals for quartic elliptic Hamiltonians

DOI10.5802/afst.915zbMath1080.37587OpenAlexW2009792712MaRDI QIDQ1299026

Moulay-Ahmed Jebrane, Frédéric Girard

Publication date: 1998

Published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AFST_1998_6_7_4_671_0

Mathematics Subject Classification ID

Pfaffian systems (58A17) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Analytic theory of abelian varieties; abelian integrals and differentials (14K20) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (4)

Linear estimate for the number of zeros of abelian integrals ⋮ The cyclicity of period annuli of a class of quintic Hamiltonian systems ⋮ Redundant Picard-Fuchs system for abelian integrals ⋮ A generalization of Françoise's algorithm for calculating higher order Melnikov functions

Cites Work

• Unnamed Item
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• Estimate of the number of zeros of an Abelian integral depending on a parameter and limit cycles
• Real analytic varieties with the finiteness property and complex abelian integrals
• Elliptic integrals and their nonoscillation
• Petrov modules and zeros of abelian integrals
• Higher order bifurcations of limit cycles
• Abelian integrals in non-symmetric perturbation of symmetric Hamiltonian vector field
• Non-oscillation of elliptic integrals
• Simple exponential estimate for the number of real zeros of complete abelian integrals
• Double exponential estimate for the number of zeros of complete Abelian integrals and rational envelopes of linear ordinary differential equations with an irreducible monodromy group
• Counting real zeros of analytic functions satisfying linear ordinary differential equations
• The number of limit cycles of polynomial deformations of a Hamiltonian vector field
• The multiplicity of limit cycles arising from perturbations of the form 𝑤’=𝑃₂/𝑄₁ of a Hamilton equation in the real and complex domain
• Intégrales asymptotiques et monodromie
• Une propriété de Chebychev pour certaines intégrales abéliennes généralisées
• Nonoscillation of Elliptic Integrals Related to Cubic Polynomials with Symmetry of Order Three
• On Second Order Bifurcations of Limit Cycles

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