Existence of inverse Jacobi multipliers around Hopf points in \(\mathbb R^3\): emphasis on the center problem

DOI10.1016/j.jde.2012.03.009zbMath1252.37040OpenAlexW2057354839MaRDI QIDQ424452

Isaac A. García, Susanna Maza, Adriana Buică

Publication date: 1 June 2012

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

Full work available at URL: https://doi.org/10.1016/j.jde.2012.03.009

zbMATH Keywords

center manifoldcenter probleminverse Jacobi multiplier

Mathematics Subject Classification ID

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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (26)

Multiple limit cycles and centers on center manifolds for Lorenz system ⋮ Integrability of vector fields versus inverse Jacobian multipliers and normalizers ⋮ 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 ⋮ Analytic partial-integrability of a symmetric Hopf-zero degeneracy ⋮ Non-autonomous inverse Jacobi multipliers and periodic orbits of planar vector fields ⋮ Nine limit cycles around a weak focus in a class of three-dimensional cubic Kukles systems ⋮ Center problem in the center manifold for quadratic and cubic differential systems in \(\mathbb{R}^3\) ⋮ Cyclicity of rigid centres on centre manifolds of three-dimensional systems ⋮ Nilpotent centers from analytical systems on center manifolds ⋮ Properties of monodromic points on center manifolds in \(\mathbb R^3\) via Lie symmetries ⋮ Inverse Jacobian multipliers and Hopf bifurcation on center manifolds ⋮ Some remarks on inverse Jacobi multipliers around Hopf singularities ⋮ Linearization of non-degenerate analytic centres in ⋮ On the integrability problem for the Hopf-zero singularity and its relation with the inverse Jacobi multiplier ⋮ A hybrid symbolic-numerical approach to the center-focus problem ⋮ Center cyclicity of Lorenz, Chen and Lü systems ⋮ Cyclicity of polynomial nondegenerate centers on center manifolds ⋮ Integrability and Dynamics of Quadratic Three-Dimensional Differential Systems Having an Invariant Paraboloid ⋮ Hopf bifurcation in 3-dimensional polynomial vector fields ⋮ CENTER PROBLEM FOR THIRD-ORDER ODEs ⋮ Centers in a Quadratic System Obtained from a Scalar Third Order Differential Equation ⋮ The center conditions and bifurcation of limit cycles at the degenerate singularity of a three-dimensional system ⋮ Inverse Jacobi Multipliers: Recent Applications in Dynamical Systems ⋮ Inverse Jacobi multipliers and first integrals for nonautonomous differential systems

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