A necessary condition in the monodromy problem for analytic differential equations on the plane

DOI10.1016/j.jsc.2006.04.007zbMath1135.34023OpenAlexW2024004049MaRDI QIDQ2457378

Maite Grau, Jaume Giné, Isaac A. García

Publication date: 23 October 2007

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2006.04.007

zbMATH Keywords

planar vector fieldmonodromycharacteristic orbit

Mathematics Subject Classification ID

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

Related Items (20)

A new algorithm for determining the monodromy of a planar differential system ⋮ ON THE DEGENERATE CENTER PROBLEM ⋮ On the centers of the weight-homogeneous polynomial vector fields on the plane ⋮ Versal unfolding of homogeneous cubic degenerate centers in strong monodromic family ⋮ ON THE CENTERS OF PLANAR ANALYTIC DIFFERENTIAL SYSTEMS ⋮ The center problem. A view from the normal form theory ⋮ Monodromy and Dulac's problem for piecewise analytical planar vector fields ⋮ Center conditions to find certain degenerate centers with characteristic directions ⋮ Nondegenerate and nilpotent centers for a cubic system of differential equations ⋮ The Poincaré map of degenerate monodromic singularities with Puiseux inverse integrating factor ⋮ Focus-center problem of planar degenerate system ⋮ Center problem for generic degenerate vector fields ⋮ Bounding the number of limit cycles for a polynomial Liénard system by using regular chains ⋮ ON THE CENTER CONDITIONS FOR ANALYTIC MONODROMIC DEGENERATE SINGULARITIES ⋮ Generalized Hopf bifurcation for planar vector fields via the inverse integrating factor ⋮ Characterization of a monodromic singular point of a planar vector field ⋮ The cyclicity of polynomial centers via the reduced Bautin depth ⋮ Center problem with characteristic directions and inverse integrating factors ⋮ A new approach to center conditions for simple analytic monodromic singularities ⋮ Monodromy of a class of analytic generalized nilpotent systems through their Newton diagram

Cites Work

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• Growth estimates for exp-log functions
• Singularities of vector fields on the plane
• Monodromy and stability of a class of degenerate planar critical points
• 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
• ON THE CENTER PROBLEM FOR DEGENERATE SINGULAR POINTS OF PLANAR VECTOR FIELDS
• Limits of Liouvillian Functions
• Finiteness theorems for limit cycles

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