An inverse approach to the center problem

DOI10.1007/s12215-018-0342-1zbMath1423.34032OpenAlexW2801991878MaRDI QIDQ2422573

Jaume Llibre, Valentín Ramírez, Rafael O. Ramírez

Publication date: 20 June 2019

Published in: Rendiconti del Circolo Matemàtico di Palermo. Serie II (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/204378

zbMATH Keywords

isochronous centercenter-focus problemweak centeranalytic planar differential systemDarboux's first integralweak condition for a centerLiapunov's constants

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) Inverse problems involving ordinary differential equations (34A55)

Related Items (6)

Research on the weak center problem of a class of \({\varLambda - \varOmega}\) differential systems ⋮ Oscillations on one dimensional time dependent center manifolds: algebraic curves approach ⋮ On the qualitative behavior of a class of the Λ − Ω differential systems ⋮ The center problem for the class of \(\varLambda-\varOmega\) differential systems ⋮ Differential equations with a given set of solutions ⋮ Center problem for \(\Lambda\)-\(\Omega\) differential systems

Cites Work

• Inverse problems in ordinary differential equations and applications
• Limit cycles of differential equations
• Smooth equivalence of germs of vector fields with a single zero eigenvalue or a pair of purely imaginary eigenvalues
• A new method for research on the center-focus problem of differential systems
• Linearization of isochronous centers
• Centers and uniform isochronous centers of planar polynomial differential systems
• An inverse approach to the center-focus problem for polynomial differential system with homogenous nonlinearities
• Qualitative theory of planar differential systems
• On the extensions of the Darboux theory of integrability
• Non-autonomous equations related to polynomial two-dimensional systems
• Coexisting Isochronous and Nonisochronous Centres
• Probleme General de la Stabilite du Mouvement. (AM-17)
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