Complete hyperelliptic integrals of the first kind and their non-oscillation

DOI10.1090/S0002-9947-03-03432-9zbMath1043.34031arXivmath/0211386OpenAlexW1585821386MaRDI QIDQ4441750

Iliya D. Iliev, Lyubomir Gavrilov

Publication date: 7 January 2004

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0211386

zbMATH Keywords

weakened 16th Hilbert problemChebyshev propertycomplete Abelian 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) 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 (19)

Limit cycles for perturbing Hamiltonian system inside piecewise smooth polynomial differential system ⋮ New criteria for the monotonicity of the ratio of two abelian integrals ⋮ Computation of expansion coefficients of Melnikov functions near a nilpotent center ⋮ A rigorous study of possible configurations of limit cycles bifurcating from a hyper-elliptic Hamiltonian of degree five ⋮ The smallest upper bound on the number of zeros of abelian integrals ⋮ Zeros of hyperelliptic integrals of the first kind for special hyperelliptic Hamiltonians of degree 7 ⋮ On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle ⋮ Limit cycle bifurcations of some Liénard systems with a cuspidal loop and a homoclinic loop ⋮ Bounding the number of zeros of certain abelian integrals ⋮ The cyclicity of period annuli of a class of quintic Hamiltonian systems ⋮ The monotonicity of ratios of some abelian integrals ⋮ The Chebyshev's property of certain hyperelliptic integrals of the first kind ⋮ Bound the number of limit cycles bifurcating from center of polynomial Hamiltonian system via interval analysis ⋮ Bifurcations on a five-parameter family of planar vector field ⋮ Limit cycles in a Liénard system with a cusp and a nilpotent saddle of order 7 ⋮ The monotonicity of the ratio of hyperelliptic integrals ⋮ Quadratic perturbations of quadratic codimension-four centers ⋮ THE NUMBER OF ZEROS OF ABELIAN INTEGRALS FOR A PERTURBATION OF HYPERELLIPTIC HAMILTONIAN SYSTEM WITH DEGENERATED POLYCYCLE ⋮ The monotonicity of the ratio of two Abelian integrals

Cites Work

• Unnamed Item
• Unnamed Item
• Chebyshev property of complete elliptic integrals and its application to Abelian integrals.
• Singularities and topology of hypersurfaces
• Le groupe de monodromie du déploiement des singularités isolées de courbes planes. I
• Petrov modules and zeros of abelian integrals
• Abelian integrals related to Morse polynomials and perturbations of plane Hamiltonian vector fields
• Bifurcation of planar vector fields and Hilbert's sixteenth problem
• Non-oscillation of elliptic integrals
• On some problems in the theory of dynamical systems
• Monodromy of isolated singularities of hypersurfaces
• Some unsolved problems in the theory of differential equations and mathematical physics
• Isochronicity of plane polynomial Hamiltonian systems
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• Tangential Hilbert problem for perturbations of hyperelliptic Hamiltonian systems
• Nonoscillation of Elliptic Integrals Related to Cubic Polynomials with Symmetry of Order Three
• The infinitesimal 16th Hilbert problem in the quadratic case

This page was built for publication: Complete hyperelliptic integrals of the first kind and their non-oscillation