Duke Mathematical Journal

Polynomial normal forms for vector fields on ℝ3

Jiazhong Yang

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The present paper is devoted to studying a class of smoothly (C) finitely determined vector fields on ℝ3. Given any such generic local system of the form $\dot{x}$=Ax+⋯, where A is a 3×3 matrix, we find the minimal possible number i(A) such that the vector field is i(A)-jet determined, and we find the number μ(A) of moduli in the C classification. We also give a list of the simplest normal forms, that is, polynomials of degree i(A) containing exactly μ(A) parameters.

Article information

Duke Math. J., Volume 106, Number 1 (2001), 1-18.

First available in Project Euclid: 13 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 34K17: Transformation and reduction of equations and systems, normal forms
Secondary: 37C15: Topological and differentiable equivalence, conjugacy, invariants, moduli, classification 37G05: Normal forms 58K45: Singularities of vector fields, topological aspects 58K50: Normal forms


Yang, Jiazhong. Polynomial normal forms for vector fields on ℝ 3. Duke Math. J. 106 (2001), no. 1, 1--18. doi:10.1215/S0012-7094-01-10611-X. https://projecteuclid.org/euclid.dmj/1092403887

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