On a theorem of Dulac

DOI10.5802/aif.1439zbMath0820.34023OpenAlexW2048125912MaRDI QIDQ1891338

Laurent Stolovitch

Publication date: 30 May 1995

Published in: Annales de l'Institut Fourier (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIF_1994__44_5_1397_0

zbMATH Keywords

normal formsholomorphic vector fieldssmall divisorsinvariant varieties

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear ordinary differential equations and systems (34A34) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Normal forms for dynamical systems (37G05) Ordinary differential equations and systems on manifolds (34C40)

Related Items

Smooth Gevrey normal forms of vector fields near a fixed point ⋮ Sectorial normalization of Poisson structures ⋮ Local analytic reduction of families of diffeomorphisms ⋮ Polynomial normal forms with exponentially small remainder for analytic vector fields ⋮ Renormalization of planar analytic saddles ⋮ Local analytic models for families of hyperbolic vector fields ⋮ Normal form of perturbations of quasihomogeneous vector fields ⋮ Classification analytique de structures de Poisson ⋮ The parameterization method for invariant manifolds. III: Overview and applications

Cites Work

• Problèmes de modules pour des équations différentielles non linéaires du premier ordre
• Materialization of resonances and divergence of normalizing series for polynomial differential equations
• On invariant manifolds of complex analytic mappings near fixed points
• Singularities that are inaccessible by geometry
• Dynamical systems I. Ordinary differential equations and smooth dynamical systems. Transl. from the Russian
• The topology of holomorphic flows with singularity
• Iteration of analytic functions
• Classification analytique des équations différentielles non linéaires résonnantes du premier ordre
• Groupes d'automorphismes de $({\bbfC},0)$ et équations différentielles $ydy+\cdots =0$
• Holonomie et intégrales premières
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