Abstract
In this paper we study on ℝn a class of smoothly (C ∞) finitely determined vector fields which admit infinite many resonant relations. We give a complete classification of all such vector fields with arbitrarily degenerated nonlinear parts.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
G. Belitskii, Smooth equivalence of germs ofC ∞ of vector fields with one zero or a pair of pure imaginary eigenvalues,Funct. Anal. Appl. 20, No.4 (1986), 253–259.
A. Bruno,Local methods in nonlinear differential equations, Springer-Verlag, 1989.
K.T. Chen, Equivalence and decomposition of vector fields about an elementary critical point,Am. J. Math. 85 (1963), 693–722.
F. Ichikawa, Finitely determined singularities of formal vector fields,Invent. Math.,66 (1982), 199–214.
F. Ichikawa, On finitely determinacy of formal vector fields,Invent. Math.,70 (1982), 4–52.
F. Takens, Singularities of vector fields,Inst. Haustes Etudes Sci. 43 (1974), 47–100.
J. Yang, Polynomial normal forms of vector fields on ℝ3 (in preparation).
J. Yang, Polynomial normal forms of vector fields,Thesis, Technion-Israel Inst. Tech. (1997).
M. Zhitomirskii,Thesis, Kharkov Univ. (1983).
Author information
Authors and Affiliations
About this article
Cite this article
Yang, J. Smooth classification of 1-resonant vector fields on ℝ3 . Bol. Soc. Bras. Mat 31, 29–43 (2000). https://doi.org/10.1007/BF01377593
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF01377593