Perturbed normalizers and Melnikov functions

DOI10.1016/j.jmaa.2018.04.004zbMath1397.34058OpenAlexW2795993454WikidataQ130041517 ScholiaQ130041517MaRDI QIDQ1748304

Adriana Buică

Publication date: 9 May 2018

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.2018.04.004

zbMATH Keywords

planar vector fieldLie bracketMelnikov functionsperturbed normalizers

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (1)

On the critical points of the flight return time function of perturbed closed orbits

Cites Work

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• The period functions' higher order derivatives
• Characterizing isochronous centres by Lie brackets
• On the equivalence of the Melnikov functions method and the averaging method
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• First derivative of the period function with applications
• Limit cycles and Lie symmetries
• On the critical periods of perturbed isochronous centers
• Bifurcation of critical periods from Pleshkan's isochrones
• regularity properties of the period function near a center of a planar vector field
• Hilbert’s 16th problem on a period annulus and Nash space of arcs
• On the period function of planar systems with unknown normalizers
• Isochronicity via normal form

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