The center problem via averaging method

DOI10.1016/j.jmaa.2008.10.029zbMath1171.34311OpenAlexW1998630324MaRDI QIDQ2518300

Isaac A. García, Jaume Giné

Publication date: 15 January 2009

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.2008.10.029

zbMATH Keywords

averaging methodbifurcation theorycenter-focus problemplanar ordinary differential equations

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) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Periodic orbits of vector fields and flows (37C27)

Related Items (9)

Bifurcation of a piecewise smooth cubic system via expansion of Melnikov function ⋮ On the limit cycles of planar polynomial system with non-rational first integral via averaging method at any order ⋮ Averaging methods of arbitrary order, periodic solutions and integrability ⋮ The number of limit cycles for some polynomial systems with multiple parameters ⋮ Sufficient and necessary center conditions for the Poincaré systems \(P(2, 2n) (n \leq 5)\) ⋮ A second order analysis of the periodic solutions for nonlinear periodic differential systems with a small parameter ⋮ Averaging theory at any order for computing periodic orbits ⋮ Periodic orbits in analytically perturbed Poisson systems ⋮ Bifurcation of Limit Cycles from the Center of a Quintic System via the Averaging Method

Cites Work

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• Limit cycles of cubic polynomial vector fields via the averaging theory
• Averaging methods for finding periodic orbits via Brouwer degree.
• Limit cycles of a perturbed cubic polynomial differential center
• The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems
• Stability of motion
• Local analytic integrability for nilpotent centers
• Averaging methods in nonlinear dynamical systems

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