Polynomial normal forms for vector fields on \(\mathbf R^3\)

DOI10.1215/S0012-7094-01-10611-XzbMath1020.34033OpenAlexW1964128065MaRDI QIDQ1847789

Jiazhong Yang

Publication date: 27 October 2002

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-01-10611-x

zbMATH Keywords

vector fieldsnumber of moduligeneric vector fieldindex of finite determinacypolynomial normal forms

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Topological and differentiable equivalence, conjugacy, moduli, classification of dynamical systems (37C15) Normal forms for dynamical systems (37G05) Singularities of vector fields, topological aspects (58K45) Normal forms on manifolds (58K50)

Related Items (9)

On smooth conjugacy of hyperbolic diffeomorphism germs ⋮ Normal forms and linearization of resonant vector fields with multiple eigenvalues ⋮ Codimension-two singularities of reversible vector fields in 3D ⋮ Linearization of resonant vector fields ⋮ On the index of finite determinacy of vector fields with resonances ⋮ Quasi-linearization of parameter-depending germs of vector fields ⋮ Smooth moduli-free normal forms of hyperbolic germs of diffeomorphisms ⋮ Unique orbital normal forms for vector fields of Hopf-zero singularity ⋮ On classification of the Poincaré type maps on \(\mathbb{R}^3\)

Cites Work

• Unnamed Item
• Smooth equivalence of germs of vector fields with a single zero eigenvalue or a pair of purely imaginary eigenvalues
• Finitely determined singularities of formal vector fields
• On finite determinacy of formal vector fields
• Normal forms for certain singularities of vectorfields
• EQUIVALENCE AND NORMAL FORMS OF GERMS OF SMOOTH MAPPINGS

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