Finitely determined singularities of formal vector fields

DOI10.1007/BF01389391zbMath0491.58025MaRDI QIDQ1167468

Fumio Ichikawa

Publication date: 1982

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/142877

zbMATH Keywords

formal first integralsaction of the formal diffeomorphisms groupfinitely determined singularity of formal vectorfields

Mathematics Subject Classification ID

Vector fields, frame fields in differential topology (57R25) Theory of singularities and catastrophe theory (58K99) Differentiable maps on manifolds (58C25) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (15)

Normal forms for singularities of vector fields ⋮ Small divisors and large multipliers ⋮ Algebras of first integrals of finitely modal singularities of vector fields ⋮ Complete transversal and formal normal forms of germs of vector fields ⋮ Local solvability of degenerate differential equations ⋮ Gevrey asymptotics of series in Mourtada-type compensators used for linearization of an analytic \({1:-1}\) resonant saddle ⋮ On the Hamiltonian structure of normal forms at elliptic equilibria of reversible vector fields in \(\mathbb{R}^4\) ⋮ Normal forms and linearization of resonant vector fields with multiple eigenvalues ⋮ Finite determinacy and polynomial normal forms for diffeomorphisms near a strongly 1-resonant fixed point ⋮ Linearization of resonant vector fields ⋮ On the index of finite determinacy of vector fields with resonances ⋮ Finite determinacy of germs of \(C^{\infty}\)-diffeomorphisms ⋮ On finite determinacy of formal vector fields ⋮ Smooth classification of 1-resonant vector fields on ?3 ⋮ Polynomial normal forms for vector fields on \(\mathbf R^3\)

Cites Work

• Singularities of vector fields
• Stability of \(C^ \infty\) mappings. III: Finitely determined map germs
• Normal forms for certain singularities of vectorfields
• Local Contractions and a Theorem of Poincare
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
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