Existence of inverse integrating factors and Lie symmetries for degenerate planar centers

DOI10.1016/j.jde.2011.08.044zbMath1298.34026OpenAlexW2044594254MaRDI QIDQ649759

Daniel Peralta-Salas, Jaume Giné

Publication date: 6 December 2011

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

Full work available at URL: https://doi.org/10.1016/j.jde.2011.08.044

zbMATH Keywords

planar vector fieldfirst integralLie symmetryinverse integrating factordegenerate center

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Geometric methods in ordinary differential equations (34A26) Symmetries, invariants of ordinary differential equations (34C14)

Related Items (17)

Invariant curves and analytic integrability of a planar vector field ⋮ Integrability of vector fields versus inverse Jacobian multipliers and normalizers ⋮ Non-formally integrable centers admitting an algebraic inverse integrating factor ⋮ On the first integrals in the center problem ⋮ Analytic integrability of cubic-linear planar polynomial differential systems ⋮ The center problem. A view from the normal form theory ⋮ Nilpotent centres via inverse integrating factors ⋮ Analytic partial-integrability of a symmetric Hopf-zero degeneracy ⋮ Nondegenerate and nilpotent centers for a cubic system of differential equations ⋮ Integrability of planar nilpotent differential systems through the existence of an inverse integrating factor ⋮ Global C^∞ integrability of quartic–linear polynomial differential systems ⋮ A method for characterizing nilpotent centers ⋮ Geometric criterium in the center problem ⋮ Quasi-homogeneous linearization of degenerate vector fields ⋮ Center problem with characteristic directions and inverse integrating factors ⋮ Some remarks on global analytic planar vector fields possessing an invariant analytic set ⋮ Regularization of sliding global bifurcations derived from the local fold singularity of Filippov systems

Cites Work

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• Local analytic integrability for nilpotent centers
• Symétrie et forme normale des centres et foyers dégénérés
• Existence and vanishing set of inverse integrating factors for analytic vector fields

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