Monodromy and stability of a class of degenerate planar critical points

DOI10.1006/jdeq.2001.4095zbMath1013.34028OpenAlexW2090352524MaRDI QIDQ1614741

Armengol Gasull, Francesc Mañosas, Víctor Mañosa

Publication date: 8 September 2002

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

Full work available at URL: https://doi.org/10.1006/jdeq.2001.4095

zbMATH Keywords

stabilityattractordegenerate critical pointmonodromy problem

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items

A new algorithm for determining the monodromy of a planar differential system ⋮ Versal unfolding of homogeneous cubic degenerate centers in strong monodromic family ⋮ Limit cycles in a class of switching system with a degenerate singular point ⋮ Center conditions to find certain degenerate centers with characteristic directions ⋮ Analytic integrability and characterization of centers for generalized nilpotent singular points. ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ Bifurcation of limit cycles and center problem for \(p : q\) homogeneous weight systems ⋮ Focus-center problem of planar degenerate system ⋮ A necessary condition in the monodromy problem for analytic differential equations on the plane ⋮ MONODROMY AND STABILITY FOR NILPOTENT CRITICAL POINTS ⋮ Center problem for generic degenerate vector fields ⋮ Integral characterization for Poincaré half-maps in planar linear systems ⋮ ON THE CENTER CONDITIONS FOR ANALYTIC MONODROMIC DEGENERATE SINGULARITIES ⋮ Integrability, degenerate centers, and limit cycles for a class of polynomial differential systems ⋮ Characterization of a monodromic singular point of a planar vector field ⋮ The problem of distinguishing between a center and a focus for nilpotent and degenerate analytic systems ⋮ A new approach to center conditions for simple analytic monodromic singularities ⋮ Monodromy of a class of analytic generalized nilpotent systems through their Newton diagram ⋮ A new criterion for controlling the number of limit cycles of some generalized Liénard equations ⋮ A note on the stability of a class of degenerate planar critical points

Cites Work

• Principal term of the monodromy transformation of a monodromic singular point is linear
• Singularities of vector fields on the plane
• The principal term of the asymptotics of the monodromy transformation: Computation in accordance with blow-up geometry
• Investigation of the behaviour of the integral curves of a system of two differential equations in the neighbourhood of a singular point
• The focus-centre problem for a type of degenerate system
• Symétrie et forme normale des centres et foyers dégénérés
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item