Cyclicity of polynomial nondegenerate centers on center manifolds

DOI10.1016/j.jde.2018.07.019zbMath1434.37030OpenAlexW2883892873MaRDI QIDQ1784835

Isaac A. García, Douglas S. Shafer, Susanna Maza

Publication date: 27 September 2018

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

Full work available at URL: http://hdl.handle.net/10459.1/65279

zbMATH Keywords

centerlimit cyclecenter manifoldcyclicity

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Dynamics induced by flows and semiflows (37C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (10)

Local bifurcation and center problem for a more generalized Lorenz system ⋮ Rigid centres on the center manifold of tridimensional differential systems ⋮ Lower bounds for the cyclicity of centers of quadratic three-dimensional systems ⋮ Bifurcation of limit cycles and isochronous centers on center manifolds for four‐dimensional systems ⋮ Cyclicity of rigid centres on centre manifolds of three-dimensional systems ⋮ Center cyclicity for some nilpotent singularities including the ℤ2-equivariant class ⋮ Center cyclicity of Lorenz, Chen and Lü systems ⋮ Cyclicity of nilpotent centers with minimum Andreev number ⋮ Center problem and \(\nu \)-cyclicity of polynomial zero-Hopf singularities with non-singular rotation axis ⋮ Hopf bifurcation in 3-dimensional polynomial vector fields

Uses Software

• SINGULAR

Cites Work

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• Ordinary Differential Equations with Applications
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