Analytic nilpotent centers as limits of nondegenerate centers revisited

DOI10.1016/j.jmaa.2016.04.046zbMath1341.34040OpenAlexW2340678696MaRDI QIDQ276846

Hector J. Giacomini, Jaume Llibre, Jaume Giné, Isaac A. García

Publication date: 4 May 2016

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2016.04.046

zbMATH Keywords

nilpotent centerPoincaré-Liapunov constants

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)

Related Items (19)

Algebraic integrability of nilpotent planar vector fields ⋮ The center problem for \(\mathbb{Z}_2\)-symmetric nilpotent vector fields ⋮ Monodromic nilpotent singular points with odd Andreev number and the center problem ⋮ Nilpotent Center in a Continuous Piecewise Quadratic Polynomial Hamiltonian Vector Field ⋮ Center conditions to find certain degenerate centers with characteristic directions ⋮ Nilpotent bi-center in continuous piecewise \(\mathbb{Z}_2\)-equivariant cubic polynomial Hamiltonian systems ⋮ Nilpotent centres via inverse integrating factors ⋮ Centers: their integrability and relations with the divergence ⋮ Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis ⋮ Nilpotent centers from analytical systems on center manifolds ⋮ Center conditions for nilpotent cubic systems using the Cherkas method ⋮ Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center ⋮ Complex integrability and linearizability of cubic \(Z_2\)-equivariant systems with two \(1:q\) resonant singular points ⋮ Center cyclicity for some nilpotent singularities including the ℤ2-equivariant class ⋮ BIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEM ⋮ Center conditions of a particular polynomial differential system with a nilpotent singularity ⋮ Formal Inverse Integrating Factor and the Nilpotent Center Problem ⋮ A new normal form for monodromic nilpotent singularities of planar vector fields ⋮ Orbitally universal centers

Cites Work

• Reversibility and classification of nilpotent centers
• The center-focus problem for a system with homogeneous nonlinearities in the case of zero eigenvalues of the linear part
• An improvement to Darboux integrability theorem for systems having a center
• A method for characterizing nilpotent centers
• The center problem for a family of systems of differential equations having a nilpotent singular point
• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• The Center and Cyclicity Problems
• Local analytic integrability for nilpotent centers
• Symétrie et forme normale des centres et foyers dégénérés
• MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS

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