Lower bounds for the local cyclicity of centers using high order developments and parallelization

DOI10.1016/j.jde.2020.08.027zbMath1460.34046OpenAlexW3088630642MaRDI QIDQ2214694

Luiz F. S. Gouveia, Joan Torregrosa

Publication date: 10 December 2020

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

Full work available at URL: https://doi.org/10.1016/j.jde.2020.08.027

zbMATH Keywords

Lyapunov constantspolynomial vector fieldcenter cyclicityhigher-order developments and parallelizationsmall-amplitude limit cycle

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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)

Related Items (11)

Lower bounds for the local cyclicity for families of centers ⋮ The local cyclicity problem: Melnikov method using Lyapunov constants ⋮ Lower bounds for the cyclicity of centers of quadratic three-dimensional systems ⋮ On the number of limit cycles of planar piecewise smooth quadratic systems with focus-parabolic type critical point ⋮ On the 16th Hilbert problem for discontinuous piecewise polynomial Hamiltonian systems ⋮ Cyclicity near infinity in piecewise linear vector fields having a nonregular switching line ⋮ Estimating the number of limit cycles for one step perturbed homogeneous degenerate centers ⋮ Cyclicity of rigid centres on centre manifolds of three-dimensional systems ⋮ Centers and limit cycles of vector fields defined on invariant spheres ⋮ Local cyclicity in low degree planar piecewise polynomial vector fields ⋮ Orbitally symmetric systems with applications to planar centers

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