The analytic and formal normal form for the nilpotent singularity. The case of generalized saddle-node

DOI10.1016/S0007-4497(02)01127-2zbMath1027.34099MaRDI QIDQ1865010

Ewa Stróżyna

Publication date: 23 March 2003

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

zbMATH Keywords

normal formmonodromy grouporbital equivalencenilpotent singularities of vector fields

Mathematics Subject Classification ID

Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies (34M55) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Related Items (12)

Analytic classification of a class of cuspidal foliations in \((\mathbb{C}^3, 0)\) ⋮ Special foliations on \(\mathbb{CP}^2\) with a unique singular point ⋮ Limit cycle bifurcations from a nilpotent focus or center of planar systems ⋮ Normal forms of double Hopf oscillators with radial nonlinearities ⋮ Orbital formal normal forms for general Bogdanov-Takens singularity. ⋮ On codimension one foliations with prescribed cuspidal separatrix ⋮ Spectral sequences and parametric normal forms ⋮ Parametric normal forms for Bogdanov-Takens singularity; the generalized saddle-node case ⋮ Vector potential normal form classification for completely integrable solenoidal nilpotent singularities ⋮ PRACTICAL COMPUTATION OF NORMAL FORMS ON CENTER MANIFOLDS AT DEGENERATE BOGDANOV–TAKENS BIFURCATIONS ⋮ Foliations on \(\mathbb{CP}^2\) with a unique singular point without invariant algebraic curves ⋮ Leaf-normal form classification for \(n\)-Tuple Hopf singularities

Cites Work

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• Problèmes de modules pour des équations différentielles non linéaires du premier ordre
• On the classification of nilpotent singularities
• The analytic and formal normal form for the nilpotent singularity
• Formal reduction of cuspidal singularities of analytic vector fields
• Singularities of vector fields
• Integrable analytic vector fields with a nilpotent linear part
• Classification analytique des équations différentielles non linéaires résonnantes du premier ordre
• Groupes d'automorphismes de $({\bbfC},0)$ et équations différentielles $ydy+\cdots =0$
• [https://portal.mardi4nfdi.de/wiki/Publication:4299146 Classification de certains feuilletages associ�s � un cusp]
• [https://portal.mardi4nfdi.de/wiki/Publication:4887461 Classification analytique d'�quations diff�rentielles ydy +...=0 et espace de modules]

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