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### Polynomial normal forms for vector fields on ℝ3

Jiazhong Yang
Source: Duke Math. J. Volume 106, Number 1 (2001), 1-18.

#### Abstract

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 =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.

First Page:
Primary Subjects: 34K17
Secondary Subjects: 37C15, 37G05, 58K45, 58K50
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1092403887
Mathematical Reviews number (MathSciNet): MR1810364
Digital Object Identifier: doi:10.1215/S0012-7094-01-10611-X
Zentralblatt MATH identifier: 1020.34033

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