scientific article; zbMATH DE number 5019876

zbMath1104.34025arXivmath/0104140MaRDI QIDQ5290230

Sergey Yu. Yakovenko

Publication date: 28 April 2006

Full work available at URL: https://arxiv.org/abs/math/0104140

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zbMATH Keywords

function fieldslimit cycleRiemann-Hilbert problemAbelian integralcyclicityHilbert's 16th problemPicard-Vessiot fieldPicard-Fuchs systembounded meandering principleconstructive finitenessquasialgebraicitytangential Hilbert's 16th problem

Mathematics Subject Classification ID

Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) (30C15) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Periodic orbits of vector fields and flows (37C27) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08) Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain (34M50) Research exposition (monographs, survey articles) pertaining to ordinary differential equations (34-02)

Related Items (10)

Limit cycles coming from some uniform isochronous centers ⋮ On extended Chebyshev systems with positive accuracy ⋮ Oscillation of linear ordinary differential equations: on a theorem of A. Grigoriev ⋮ Phase portraits of separable quadratic systems and a bibliographical survey on quadratic systems ⋮ Principal Poincaré-Pontryagin function of polynomial perturbations of the Hamiltonian triangle ⋮ Multiplicity operators ⋮ Polynomial bounds for the oscillation of solutions of Fuchsian systems ⋮ On the number of zeros of Abelian integrals. A constructive solution of the infinitesimal Hilbert sixteenth problem ⋮ Abelian integrals and limit cycles ⋮ A new Chebyshev criterion and its application to planar differential systems

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