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15 January 2001 Polynomial normal forms for vector fields on ℝ3
Jiazhong Yang
Duke Math. J. 106(1): 1-18 (15 January 2001). DOI: 10.1215/S0012-7094-01-10611-X

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 $\dot{x}$=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.

Citation

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Jiazhong Yang. "Polynomial normal forms for vector fields on ℝ3." Duke Math. J. 106 (1) 1 - 18, 15 January 2001. https://doi.org/10.1215/S0012-7094-01-10611-X

Information

Published: 15 January 2001
First available in Project Euclid: 13 August 2004

zbMATH: 1020.34033
MathSciNet: MR1810364
Digital Object Identifier: 10.1215/S0012-7094-01-10611-X

Subjects:
Primary: 34K17
Secondary: 37C15, 37G05, 58K45, 58K50

Rights: Copyright © 2001 Duke University Press

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Vol.106 • No. 1 • 15 January 2001
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