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Analytic linearizability of some resonant vector fields
Author(s):
J.
Basto-Gonçalves;
I.
Cruz
Journal:
Proc. Amer. Math. Soc.
129
(2001),
2473-2481.
MSC (1991):
Primary 58F36, 32S65, 34A20, 34A34
Posted:
December 7, 2000
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Abstract:
A method allowing the linearization of vector fields with resonant eigenvalues is presented, the admissible nonlinearities being characterized by conditions that are easy to check.
References:
-
- 1.
- V. Arnold. Geometrical Methods in the Theory of Ordinary Differential Equations. Springer-Verlag, 1983. MR 84d:58023
- 2.
- J. Basto-Gonçalves, I. Cruz. Analytic
 -linearizability of some resonant Poisson structures. Letters in Math. Physics, 49, 1 (1999), 59-66. CMP 2000:04 - 3.
- A. Brjuno. Analytical form of differential equations. Trans. Moscow Math. Soc., 25 (1971),131-288. MR 51:13365
- 4.
- I. Cruz. The Local Structure of Poisson Manifolds. Ph. D. thesis, Warwick (U.K.), 1995.
- 5.
- J. Dieudonné. Foundations of Modern Analysis. Academic Press, 1960. MR 22:11074
- 6.
- J.P. Dufour. Linéarisation de certaines structures de Poisson. Journal of Differential Geometry, 32:415-428, 1990. MR 91m:58139
- 7.
- E. Hille. Ordinary Differential Equations in the Complex Domain. Wiley-Interscience, 1976. MR 58:17266
- 8.
- R. Roussarie. Modèles locaux de champs et de formes. Astérisque, 30, 1975. MR 55:13444
- 9.
- S. Sternberg. On the structure of local homeomorphisms of Euclidean space II. American Journal of Mathematics, 80 (1958), 623-631. MR 20:3336
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Additional Information:
J.
Basto-Gonçalves
Affiliation:
Departamento de Matemática Aplicada, Centro de Matemática Aplicada da Universidade do Porto, R. das Taipas, 135, 4050-600 Porto, Portugal
Email:
jbgoncal@fc.up.pt
I.
Cruz
Affiliation:
Departamento de Matemática Aplicada, Centro de Matemática Aplicada da Universidade do Porto, R. das Taipas, 135, 4050-600 Porto, Portugal
Email:
imcruz@fc.up.pt
DOI:
10.1090/S0002-9939-00-05796-8
PII:
S 0002-9939(00)05796-8
Received by editor(s):
August 16, 1999
Received by editor(s) in revised form:
December 7, 1999
Posted:
December 7, 2000
Additional Notes:
The first author's research was supported by JNICT, and by the Calouste Gulbenkian Foundation.
The second author's research was supported by JNICT
Communicated by:
Carmen Chicone
Copyright of article:
Copyright
2000,
American Mathematical Society
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