The center conditions for a perturbed cubic center via the fourth-order Melnikov function

DOI10.1007/s13398-022-01333-2zbMath1496.34065OpenAlexW4301586051MaRDI QIDQ2081244

Rasoul Asheghi

Publication date: 12 October 2022

Published in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Matemáticas. RACSAM (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s13398-022-01333-2

zbMATH Keywords

center problemMelnikov functionsquadratic perturbations

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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Cites Work

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• The third order Melnikov function of a quadratic center under quadratic perturbations
• Bifurcation of limit cycles from a polynomial non-global center
• The third order Melnikov function of a cubic integrable system under quadratic perturbations
• Using Melnikov functions of any order for studying limit cycles
• Higher order Melnikov functions for studying limit cycles of some perturbed elliptic Hamiltonian vector fields
• Limit cycles of a perturbed cubic polynomial differential center
• The number of limit cycles due to polynomial perturbations of the harmonic oscillator
• Successive derivatives of a first return map, application to the study of quadratic vector fields
• Averaging analysis of a perturbated quadratic center

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