An explicit expression for the first return map in the center problem

DOI10.1016/j.jde.2004.04.002zbMath1066.34026OpenAlexW1987997039MaRDI QIDQ703817

Alexander Brudnyi

Publication date: 11 January 2005

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

Full work available at URL: https://doi.org/10.1016/j.jde.2004.04.002

zbMATH Keywords

first return mapcenter-focus problemplane systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (14)

Shuffle and Faà di Bruno Hopf algebras in the center problem for ordinary differential equations ⋮ An algebraic model for the center problem ⋮ Iterated integrals, Gelfand-Leray residue, and first return mapping ⋮ Centers for trigonometric Abel equations ⋮ Vanishing of higher-order moments on Lipschitz curves ⋮ Formal paths, iterated integrals and the center problem for ordinary differential equations ⋮ EXPLICIT DERIVATION OF RETURN MAPS FOR PLANAR VECTOR FIELDS WITH NILPOTENT LINEAR PART WITH A CENTER OR A FOCUS ⋮ On center sets of ODEs determined by moments of their coefficients ⋮ On the multiplicity of algebraic limit cycles ⋮ Center conditions at infinity for Abel differential equations ⋮ Orbitally universal centers ⋮ Universal curves in the center problem for Abel differential equations ⋮ The return map for a planar vector field with nilpotent linear part: a direct and explicit derivation ⋮ A counterexample to the composition condition conjecture for polynomial Abel differential equations

Cites Work

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• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• The successive derivatives of the period function of a plane vector field
• An algebraic approach to the classification of centers in polynomial Liénard systems
• The problem of center for resonant singular points of polynomial vector fields
• Conditions for a centre in a simple class of cubic systems
• Composition conditions and center problem
• Algebraic Particular Integrals, Integrability and the Problem of the Center
• Non-autonomous equations related to polynomial two-dimensional systems
• Composition conditions for two-dimensional polynomial systems

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