The center-focus problem and reversibility

DOI10.1006/jdeq.2000.3931zbMath0994.34020OpenAlexW2074143195MaRDI QIDQ5944088

Marco Antonio Teixeira, Jiazhong Yang

Publication date: 29 September 2002

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

Full work available at URL: https://doi.org/10.1006/jdeq.2000.3931

zbMATH Keywords

centerfocusnormal formsreversibilityinvolutionanalytic vector fieldmonodromy conditions

Mathematics Subject Classification ID

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

Related Items (32)

Analytic integrability of some examples of degenerate planar vector fields ⋮ Center conditions and limit cycles for a class of nilpotent-Poincarè systems ⋮ Analytic integrability inside a family of degenerate centers ⋮ Bifurcation of limit cycles in a cubic-order planar system around a nilpotent critical point ⋮ The reversibility and the center problem ⋮ The center problem and time-reversibility with respect to a quadratic involution for a class of polynomial differential systems with order 2 or 3 ⋮ The center problem. A view from the normal form theory ⋮ New criterions on stability and order of analytic nilpotent foci ⋮ Polynomial Liénard systems with a nilpotent global center ⋮ Centers: their integrability and relations with the divergence ⋮ Minimum number of ideal generators for a linear center perturbed by homogeneous polynomials ⋮ Centers of quasi-homogeneous polynomial planar systems ⋮ Analytic integrability and characterization of centers for generalized nilpotent singular points. ⋮ Local bifurcation of limit cycles and center problem for a class of quintic nilpotent systems ⋮ Analytic integrability for some degenerate planar vector fields ⋮ Generalized cofactors and nonlinear superposition principles ⋮ Calculation of singular point quantities at infinity for a type of polynomial differential systems ⋮ A class of reversible cubic systems with an isochronous center ⋮ Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center ⋮ Limit cycles and analytic centers for a family of \(4n - 1\) degree systems with generalized nilpotent singularities ⋮ Editorial: Some classes of function spaces, their properties, and their applications 2014 ⋮ Analytic nilpotent centers with analytic first integral ⋮ Reversibility and quasi-homogeneous normal forms of vector fields ⋮ Completely symmetric centers ⋮ The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems ⋮ Geometric criterium in the center problem ⋮ Characterizing orbital-reversibility through normal forms ⋮ On orbital-reversibility for a class of planar dynamical systems ⋮ Limit cycle bifurcations and analytic center conditions for a class of generalized nilpotent systems ⋮ Periodic solutions of a 2D-autonomous system using Mathematica\(^{\copyright}\) ⋮ Families of periodic orbits in resonant reversible systems ⋮ Reversibility in polynomial systems of ODE's

Cites Work

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• Smooth equivalence of germs of vector fields with a single zero eigenvalue or a pair of purely imaginary eigenvalues
• The classification of reversible cubic systems with center
• Five limit cycles for a simple cubic system
• The analytic and formal normal form for the nilpotent singularity
• Singularities of vector fields
• On the Paper of Jin and Wang Concerning the conditions for a Centre in certain Cubic Systems
• Symétrie et forme normale des centres et foyers dégénérés

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