Two-dimensional Fuchsian systems and the Chebyshev property.

DOI10.1016/S0022-0396(02)00116-XzbMath1046.34056arXivmath/0111236OpenAlexW2133072362MaRDI QIDQ1874500

Iliya D. Iliev, Lyubomir Gavrilov

Publication date: 25 May 2003

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0111236

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (14)

On extended Chebyshev systems with positive accuracy ⋮ The smallest upper bound on the number of zeros of abelian integrals ⋮ The cyclicity of period annuli of a class of quadratic reversible systems with two centers ⋮ On the number of limit cycles in small perturbations of a class of hyper-elliptic Hamiltonian systems with one nilpotent saddle ⋮ The cyclicity and period function of a class of quadratic reversible Lotka-Volterra system of genus one ⋮ Number of zeros of complete abelian integrals for a primitive rational polynomial with non-trivial global monodromy ⋮ Bounding the number of zeros of certain abelian integrals ⋮ On the Chebyshev property for a new family of functions ⋮ On the number of zeros of abelian integrals for a kind of quartic Hamiltonians ⋮ Perturbations of non-Hamiltonian reversible quadratic systems with cubic orbits ⋮ A Chebyshev criterion for Abelian integrals ⋮ New family of abelian integrals satisfying Chebyshev property ⋮ Further study on Horozov-Iliev's method of estimating the number of limit cycles ⋮ A new Chebyshev criterion and its application to planar differential systems

Cites Work

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• Elliptic integrals and their nonoscillation
• Zeroes of complete elliptic integrals for 1:2 resonance
• On the nonoscillation of elliptic integrals
• Abelian integrals related to Morse polynomials and perturbations of plane Hamiltonian vector fields
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• Nonoscillation of Elliptic Integrals Related to Cubic Polynomials with Symmetry of Order Three

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