The center problem. A view from the normal form theory

DOI10.1016/j.jmaa.2015.09.027zbMath1329.34071OpenAlexW1731989454MaRDI QIDQ890527

Antonio Algaba, Cristóbal García, Estanislao Gamero

Publication date: 10 November 2015

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.2015.09.027

zbMATH Keywords

integrabilityreversibilitycenter problemLie symmetryinverse integrating factororbital normal form

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (9)

An inverse approach to the center-focus problem for polynomial differential system with homogenous nonlinearities ⋮ Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor ⋮ Analytic integrability around a nilpotent singularity ⋮ Center problem for generic degenerate vector fields ⋮ On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier ⋮ Characterizing orbital-reversibility through normal forms ⋮ Center conditions of a particular polynomial differential system with a nilpotent singularity ⋮ Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system ⋮ A new normal form for monodromic nilpotent singularities of planar vector fields

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