On saddle-loop bifurcations of limit cycles in perturbations of quadratic Hamiltonian systems
From MaRDI portal
Publication:1336337
DOI10.1006/jdeq.1994.1115zbMath0808.34041OpenAlexW1997634909MaRDI QIDQ1336337
Publication date: 28 November 1994
Published in: Journal of Differential Equations (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1006/jdeq.1994.1115
bifurcationspolynomial vector fieldsHilbert's 16th problemnumber of limit cyclesquadratic Hamiltonian vector fields on the plane
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)
Related Items
Limit cycle bifurcations by perturbing a quadratic integrable system with a triangle ⋮ The cyclicity of quadratic reversible systems with a center of genus one and non-Morsean point ⋮ Unfolding of a quadratic integrable system with two centers and two unbounded heteroclinic loops ⋮ Perturbations of quadratic Hamiltonian systems with symmetry ⋮ Analysis and synthesis of oscillator systems described by a perturbed double-well Duffing equation ⋮ Cyclicity of planar homoclinic loops and quadratic integrable systems ⋮ Higher order Melnikov functions for studying limit cycles of some perturbed elliptic Hamiltonian vector fields ⋮ Heteroclinic bifurcation of limit cycles in perturbed cubic Hamiltonian systems by higher-order analysis ⋮ Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems ⋮ Uniqueness of limit cycles and quotients of abelian integrals ⋮ On the cyclicity of a 2-polycycle for quadratic systems ⋮ Bifurcations and distribution of limit cycles which appear from two nests of periodic orbits ⋮ Center configurations of Hamiltonian cubic systems ⋮ Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point ⋮ Unfolding of a quadratic integrable system with a homoclinic loop ⋮ EIGHT LIMIT CYCLES AROUND A CENTER IN QUADRATIC HAMILTONIAN SYSTEM WITH THIRD-ORDER PERTURBATION ⋮ Cyclicity of homoclinic loops and degenerate cubic Hamiltonians ⋮ Perturbations of quadratic Hamiltonian two-saddle cycles ⋮ A unified proof of the weakened Hilbert 16th problem for \(n=2\)
