Analytic linearizability of some resonant vector fields
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- by J. Basto-Gonçalves and I. Cruz PDF
- Proc. Amer. Math. Soc. 129 (2001), 2473-2481 Request permission
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
- V. I. Arnol′d, Geometrical methods in the theory of ordinary differential equations, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 250, Springer-Verlag, New York-Berlin, 1983. Translated from the Russian by Joseph Szücs; Translation edited by Mark Levi. MR 695786, DOI 10.1007/978-1-4684-0147-9
- J. Basto-Gonçalves, I. Cruz. Analytic $k$-linearizability of some resonant Poisson structures. Letters in Math. Physics, 49, 1 (1999), 59-66.
- A. D. Brjuno, Analytic form of differential equations. I, II, Trudy Moskov. Mat. Obšč. 25 (1971), 119–262; ibid. 26 (1972), 199–239 (Russian). MR 0377192
- I. Cruz. The Local Structure of Poisson Manifolds. Ph. D. thesis, Warwick (U.K.), 1995.
- J. Dieudonné, Foundations of modern analysis, Pure and Applied Mathematics, Vol. X, Academic Press, New York-London, 1960. MR 0120319
- J.-P. Dufour, Linéarisation de certaines structures de Poisson, J. Differential Geom. 32 (1990), no. 2, 415–428 (French, with English summary). MR 1072912
- Einar Hille, Ordinary differential equations in the complex domain, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1976. MR 0499382
- Robert Roussarie, Modèles locaux de champs et de formes, Astérisqûe, No. 30, Société Mathématique de France, Paris, 1975. With an English summary. MR 0440570
- Shlomo Sternberg, On the structure of local homeomorphisms of euclidean $n$-space. II, Amer. J. Math. 80 (1958), 623–631. MR 96854, DOI 10.2307/2372774
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
- Received by editor(s): August 16, 1999
- Received by editor(s) in revised form: December 7, 1999
- Published electronically: 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 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 2473-2481
- MSC (1991): Primary 58F36, 32S65, 34A20, 34A34
- DOI: https://doi.org/10.1090/S0002-9939-00-05796-8
- MathSciNet review: 1823934