Abstract
The goal of this paper is to present a generalization of the POINCARE - DULAC theorem about normal forms of vectors fields near an equilibrium point.
We show that a derivation whose terms are formal power series in non commutative variables without constant terms can be transformed by a change of variables into a normal form whose “non - linear” terms are “resonnant”.
This research was supported by the french PRC Math-Info and the IMAG project DESIR - II.
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References
H. Poincaré: Thèse (1879). Oeuvres I, Gauthier-Villars, Paris, 1928, 69–129
T. Carleman, Ark. Math. Astron. Fys. 22B, 1 (1932)
R. Bellman and J.M. Richardson Quart. Appl. Math. 20 (1963), 333–339
W.-H. Steeb and F. Wilhelm Journal of Mathematical Analysis and Applications 77, 601–611 (1980)
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© 1991 Springer-Verlag
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Della Dora, J., Stolovitch, L. (1991). Poincare normal form and carleman linearization. In: Jacob, G., Lamnabhi-Lagarrigue, F. (eds) Algebraic Computing in Control. Lecture Notes in Control and Information Sciences, vol 165. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006946
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DOI: https://doi.org/10.1007/BFb0006946
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