On the number of limit cycles in small perturbations of a piecewise linear Hamiltonian system with a heteroclinic loop

DOI10.1007/s11401-016-0946-8zbMath1342.34051OpenAlexW2416845099MaRDI QIDQ266197

Feng Liang, Mao'an Han

Publication date: 13 April 2016

Published in: Chinese Annals of Mathematics. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11401-016-0946-8

zbMATH Keywords

bifurcationlimit cycleChebyshev systemMelnikov functionheteroclinic looppiecewise smooth 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) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (4)

Limit Cycles Appearing From Piecewise Smooth Perturbations to a Reversible Nonlinear Center ⋮ Limit cycles for perturbing a piecewise linear Hamiltonian system with one or two saddles ⋮ The Maximal Number of Limit Cycles in Perturbations of Piecewise Linear Hamiltonian Systems with Two Saddles ⋮ Bifurcation of limit cycles of a piecewise smooth Hamiltonian system

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