Symétrie et forme normale des centres et foyers dégénérés

From MaRDI portal
Publication:4746850

DOI10.1017/S0143385700001553zbMath0509.34027OpenAlexW2119673826MaRDI QIDQ4746850

Robert Moussu

Publication date: 1982

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0143385700001553




Related Items (87)

Analytic integrability of a class of nilpotent cubic systemsAnalytic integrability of some examples of degenerate planar vector fieldsMonodromy and stability of a class of degenerate planar critical pointsMultiple limit cycles bifurcation from the degenerate singularity for a class of three-dimensional systemsSymmetries of center singularities of plane vector fieldsAnalytic nilpotent centers as limits of nondegenerate centers revisitedCenter conditions and limit cycles for a class of nilpotent-Poincarè systemsAnalytic integrability inside a family of degenerate centersReversibility and classification of nilpotent centersGenerating limit cycles from a nilpotent critical point via normal formsOn the centers of the weight-homogeneous polynomial vector fields on the planeBifurcation of limit cycles in a cubic-order planar system around a nilpotent critical pointCyclicity of a simple focus via the vanishing multiplicity of inverse integrating factorsCenter conditions and bifurcation of limit cycles at degenerate singular points in a quintic polynomial differential systemMonodromy, center-focus and integrability problems for quasi-homogeneous polynomial systemsNon-formally integrable centers admitting an algebraic inverse integrating factorBifurcation of limit cycles in a quintic system with ten parametersMonodromic nilpotent singular points with odd Andreev number and the center problemBi-center problem and bifurcation of limit cycles from nilpotent singular points in \(Z_{2}\)-equivariant cubic vector fieldsLocal bifurcation of limit cycles and integrability of a class of nilpotent systemsOn the first integrals in the center problemThe three-dimensional center problem for the zero-Hopf singularityThe center problem. A view from the normal form theoryNew criterions on stability and order of analytic nilpotent fociPolynomial Liénard systems with a nilpotent global centerThe Poincaré center problemNilpotent centres via inverse integrating factorsLimit cycle bifurcations from a nilpotent focus or center of planar systemsNondegenerate and nilpotent centers for a cubic system of differential equationsCenters: their integrability and relations with the divergenceCenters of quasi-homogeneous polynomial planar systemsThe Poincaré map of degenerate monodromic singularities with Puiseux inverse integrating factorCenter conditions and bifurcation of limit cycles at three-order nilpotent critical point in a cubic Lyapunov systemAnalytical integrability of the Rikitake systemBalanced coordinates for spiraling dynamics.Limit cycles in a quartic system with a third-order nilpotent singular pointAnalytic integrability and characterization of centers for generalized nilpotent singular points.Bifurcation of limit cycles and center conditions for two families of Kukles-like systems with nilpotent singularitiesExistence of inverse integrating factors and Lie symmetries for degenerate planar centersLocal bifurcation of limit cycles and center problem for a class of quintic nilpotent systemsCenter conditions and bifurcation of limit cycles at three-order nilpotent critical point in a septic Lyapunov systemAnalytic integrability for some degenerate planar vector fieldsAlgebraic nonsolvability of the problem of existence of holomorphic first integralsCalculation of singular point quantities at infinity for a type of polynomial differential systemsCenter conditions for nilpotent cubic systems using the Cherkas methodNine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent centerA KIND OF BIFURCATION OF LIMIT CYCLES FROM A NILPOTENT CRITICAL POINTLimit cycles and analytic centers for a family of \(4n - 1\) degree systems with generalized nilpotent singularitiesEditorial: Some classes of function spaces, their properties, and their applications 2014The problem of distinguishing between a centre and a focus in the space of vector fields with given Newton diagramThe center problem for a family of systems of differential equations having a nilpotent singular pointON THE CENTER CONDITIONS FOR ANALYTIC MONODROMIC DEGENERATE SINGULARITIESCenter-focus and Hopf bifurcation for a class of quartic Kukles-like systemsBIFURCATION OF LIMIT CYCLES AT A NILPOTENT CRITICAL POINT IN A SEPTIC LYAPUNOV SYSTEMAnalytic nilpotent centers with analytic first integralOn some open problems in planar differential systems and Hilbert's 16th problemAnalytic integrability of a modified Michaelis-Menten equationGeneralized Hopf bifurcation for planar vector fields via the inverse integrating factorThe center-focus problem and reversibilityBifurcation diagram and stability for a one-parameter family of planar vector fieldsA method for characterizing nilpotent centersThe problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systemsCenter conditions and bifurcation of limit cycles at three-order nilpotent critical point in a seventh degree Lyapunov systemCenter type performance of differentiable vector fields in the planeGeometric criterium in the center problemFormal Inverse Integrating Factor and the Nilpotent Center ProblemAnalytic Integrability of Two Lopsided SystemsLocal bifurcation of limit cycles and integrability of a class of nilpotent systems of differential equationsLimit cycle bifurcations and analytic center conditions for a class of generalized nilpotent systemsAnalytic integrability of quadratic–linear polynomial differential systemsA new normal form for monodromic nilpotent singularities of planar vector fieldsANALYTIC INTEGRABILITY OF NILPOTENT CUBIC SYSTEMS WITH DEGENERATE INFINITYAn algebraic approach to the classification of centers in polynomial Liénard systemsApproximate calculation of the coefficients of the Dulac seriesNEW STUDY ON THE CENTER PROBLEM AND BIFURCATIONS OF LIMIT CYCLES FOR THE LYAPUNOV SYSTEM (II)Center problem with characteristic directions and inverse integrating factorsAsymptotic expansions for a degenerate canard explosionAlgebraic criterion for the existence of a center at a monodromic singular point of a polynomial Liénard systemA new approach to center conditions for simple analytic monodromic singularitiesAnalytic first integrals for generalized Raychaudhuri equationsThe center conditions and bifurcation of limit cycles at the degenerate singularity of a three-dimensional systemDouble Bifurcation of Nilpotent FocusNew Double Bifurcation of Nilpotent FocusOn the analytic solvability of the problem of distinguishing between center and focusThe analytic and formal normal form for the nilpotent singularityFormal and analytical integrability of the Bianchi IX systemA note on the stability of a class of degenerate planar critical points



Cites Work


This page was built for publication: Symétrie et forme normale des centres et foyers dégénérés