First-order perturbation for multi-parameter center families

DOI10.1016/j.jde.2021.11.035zbMath1493.34106OpenAlexW3216758472MaRDI QIDQ2062036

Joan Torregrosa, Jackson Itikawa, Regilene D. S. Oliveira

Publication date: 22 December 2021

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

Full work available at URL: https://doi.org/10.1016/j.jde.2021.11.035

zbMATH Keywords

averaging theoryMelnikov functionsmulti-parameter perturbation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Cites Work

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• Centennial History of Hilbert's 16th Problem
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Differentiation Under the Integral Sign
• Abelian integrals and limit cycles
• Averaging analysis of a perturbated quadratic center

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