On a Żołądek theorem

DOI10.1134/S0012266108020158zbMath1186.34042OpenAlexW2113018613MaRDI QIDQ843674

Yu. L. Bondar', A. P. Sadovskij

Publication date: 15 January 2010

Published in: Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0012266108020158

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (17)

Lower bounds for the local cyclicity for families of centers ⋮ Bifurcation of limit cycles in a cubic-order planar system around a nilpotent critical point ⋮ Twelve Limit Cycles in 3D Quadratic Vector Fields with Z3 Symmetry ⋮ An Improvement on the Number of Limit Cycles Bifurcating from a Nondegenerate Center of Homogeneous Polynomial Systems ⋮ The local cyclicity problem: Melnikov method using Lyapunov constants ⋮ 24 crossing limit cycles in only one nest for piecewise cubic systems ⋮ Weak-foci of high order and cyclicity ⋮ Bifurcation of small limit cycles in cubic integrable systems using higher-order analysis ⋮ Lower bounds for the local cyclicity of centers using high order developments and parallelization ⋮ Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center ⋮ Parallelization of the Lyapunov constants and cyclicity for centers of planar polynomial vector fields ⋮ New lower bounds for the Hilbert numbers using reversible centers ⋮ Local cyclicity in low degree planar piecewise polynomial vector fields ⋮ Complex isochronous centers and linearization transformations for cubic \(Z_2\)-equivariant planar systems ⋮ Twelve limit cycles around a singular point in a planar cubic-degree polynomial system ⋮ Hopf bifurcation in 3-dimensional polynomial vector fields ⋮ BIFURCATION OF LIMIT CYCLES AND ISOCHRONOUS CENTERS FOR A QUARTIC SYSTEM

Cites Work

• Eleven small limit cycles in a cubic vector field

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