Algebraic geometry of the center-focus problem for Abel differential equations

DOI10.1017/etds.2014.94zbMath1362.37055arXiv1211.1296OpenAlexW3098027397WikidataQ115337174 ScholiaQ115337174MaRDI QIDQ2805055

Yosef Yomdin, Miriam Briskin, Fedor Pakovitch

Publication date: 9 May 2016

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.1296

zbMATH Keywords

planar vector fieldmoment equationsAbel differential equationcomposition algebracenter-focus problemMelnikov coefficients

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Geometric methods in ordinary differential equations (34A26) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25)

Related Items (8)

New criterions on stability and order of analytic nilpotent foci ⋮ On the center problem for generalized Abel equations ⋮ Weak and strong composition conditions for the Abel differential equation ⋮ Parametric center-focus problem for Abel equation ⋮ On decompositions of trigonometric polynomials ⋮ Solution of the parametric center problem for the Abel differential equation ⋮ Centers of planar generalized Abel equations ⋮ Algebraic criterion for the existence of a center at a monodromic singular point of a polynomial Liénard system

Cites Work

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• Universal centres and composition conditions
• Generalized ‘second Ritt theorem’ and explicit solution of the polynomial moment problem
• On the trigonometric moment problem
• On the center problem for ordinary differential equations
• Polynomial Substitutions

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