On the Number of Limit Cycles Bifurcated from Some Hamiltonian Systems with a Double Homoclinic Loop and a Heteroclinic Loop

DOI10.1142/S0218127417500559zbMath1366.34047MaRDI QIDQ5275064

Pegah Moghimi, Rasool Kazemi, Rasoul Asheghi

Publication date: 10 July 2017

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

asymptotic expansionbifurcationlimit cycleMelnikov functionHamiltonian 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) Asymptotic expansions of solutions to ordinary differential equations (34E05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (3)

On the Number of Limit Cycles Bifurcated from a Near-Hamiltonian System with a Double Homoclinic Loop of Cuspidal Type Surrounded by a Heteroclinic Loop ⋮ On the algebraic structure and the number of zeros of abelian integral for a class of Hamiltonians with degenerate singularities ⋮ On the number of limit cycles bifurcated from some non-polynomial Hamiltonian systems

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