Degenerate homoclinic cycles in perturbations of quadratic Hamiltonian systems

DOI10.1088/0951-7715/2/3/002zbMath0677.58038OpenAlexW2035927581MaRDI QIDQ3833313

John Guckenheimer, Dana Schlomiuk, Richard H. Rand

Publication date: 1989

Published in: Nonlinearity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1088/0951-7715/2/3/002

zbMATH Keywords

limit cycleshomoclinic orbitintegrable perturbationsplanar quadratic Hamiltonian systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Local and nonlocal bifurcation theory for dynamical systems (37G99)

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Center conditions and bifurcation of limit cycles at degenerate singular points in a quintic polynomial differential system ⋮ Analysis and synthesis of oscillator systems described by a perturbed double-well Duffing equation ⋮ REDUCE and the bifurcation of limit cycles ⋮ Algebraic Particular Integrals, Integrability and the Problem of the Center ⋮ Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems ⋮ Computing centre conditions for certain cubic systems ⋮ Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation ⋮ Symbolic computation of limit cycles associated with Hilbert's 16th problem ⋮ Cyclicity of homoclinic loops and degenerate cubic Hamiltonians ⋮ On the equivalence and qualitative behavior of the rational differential equations

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