On the bifurcation of limit cycles due to polynomial perturbations of Hamiltonian centers

DOI10.1007/s00009-017-0857-2zbMath1375.34063OpenAlexW2594922617MaRDI QIDQ2362974

Claudia Valls, Jaume Llibre, Ilker E. Colak

Publication date: 12 July 2017

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/182528

zbMATH Keywords

centerlimit cyclepolynomial systemMelnikov functionHamiltonian systemplanar systemordinary differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) 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)

Related Items

Remarks on a class of generalized Liénard planar systems, A LINEAR ESTIMATION TO THE NUMBER OF ZEROS FOR ABELIAN INTEGRALS IN A KIND OF QUADRATIC REVERSIBLE CENTERS OF GENUS ONE

Cites Work

• Limit cycles for a class of second order differential equations
• Center problem for systems with two monomial nonlinearities
• Periodic orbits and their stability in the Rössler prototype-4 system
• On the limit cycles bifurcating from a quadratic reversible center of genus one
• 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
• Unnamed Item
• Unnamed Item
• Unnamed Item