The composition conjecture for Abel equation

DOI10.1016/j.exmath.2009.02.002zbMath1190.34048OpenAlexW1967089765WikidataQ123238329 ScholiaQ123238329MaRDI QIDQ1028222

M. A. M. Alwash

Publication date: 30 June 2009

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2009.02.002

zbMATH Keywords

periodic solutionmomentAbel differential equationcomposition conjecturecenter conditiontwo-dimensional polynomial system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (16)

The center problem and composition condition for Abel differential equations ⋮ Shuffle and Faà di Bruno Hopf algebras in the center problem for ordinary differential equations ⋮ An explicit bound of the number of vanishing double moments forcing composition ⋮ A numerical approach for solving generalized Abel-type nonlinear differential equations ⋮ On the composition center for a class of rigid system ⋮ A new approach for the study of limit cycles ⋮ Centers for trigonometric Abel equations ⋮ On the center problem for generalized Abel equations ⋮ Weak and strong composition conditions for the Abel differential equation ⋮ A partial positive answer to a Lijun-Yun conjecture ⋮ RESEARCH ON THE COMPOSITION CENTER OF A CLASS OF RIGID DIFFERENTIAL SYSTEMS ⋮ Polynomial differential equations with piecewise linear coefficients ⋮ Algebraic geometry of the center-focus problem for Abel differential equations ⋮ On the center-focus problem for a family of high-order polynomial differential systems ⋮ Universal curves in the center problem for Abel differential equations ⋮ A counterexample to the composition condition conjecture for polynomial Abel differential equations

Cites Work

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• Center conditions at infinity for Abel differential equations
• Cubic systems and Abel equations
• Qualitative theory of planar differential systems
• On polynomials orthogonal to all powers of a given polynomial on a segment
• Solution of the polynomial moment problem
• On the center conditions of certain cubic systems
• Generalized centre conditions and multiplicities for polynomial Abel equations of small degrees
• A counterexample to the “composition conjecture"
• Non-autonomous equations related to polynomial two-dimensional systems
• On a condition for a centre of cubic non-autonomous equations

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