Abstract
We consider smooth normalization problems for systems of ordinary differential equations whose linear part has one zero eigenvalue, while the other eigenvalues lie outside the imaginary axis.
Similar content being viewed by others
REFERENCES
A. D. Bryuno, A Local Method for Nonlinear Analysis of Differential Equations [in Russian], Nauka, Moscow, 1979.
V. S. Samovol, “Equivalence of systems of differential equations in a neighborhood of a singular point,” Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.], 44 (1982), 213–234.
V. A. Nikishkin, “C ∞-equivalence of systems of differential equations in a neighborhood of a singular point of a “degenerate knot” type,” Vestnik Moskov. Univ. Ser. I Mat. Mekh. [Moscow Univ. Math. Bull.] (1976), no. 1, 27–35.
Yu. N. Bibikov, “On the reducibility of a system of two differential equations to normal form,” Differentsialľnye Uravneniya [Differential Equations], 7 (1971), no. 10, 1899–1902.
Yu. N. Bibikov, “On a critical case in the theory of stability of motion,” Differentsialľnye Uravneniya [Differential Equations], 9 (1973), no. 12, 2123–2135.
A. N. Kuznetsov, “Differentiable solutions of degenerating systems of ordinary equations,” Funktsional. Anal. i Prilozhen. [Functional Anal. Appl.], 6 (1972), no. 2, 41–51.
V. S. Samovol, “A necessary and sufficient condition for a smooth linearization of an autonomous system on the plane in a neighborhood of a singular point,” Mat. Zametki [Math. Notes], 46 (1989), no. 1, 67–77.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Samovol, V.S. Normal Form of Autonomous Systems with One Zero Eigenvalue. Mathematical Notes 75, 660–668 (2004). https://doi.org/10.1023/B:MATN.0000030974.08984.21
Issue Date:
DOI: https://doi.org/10.1023/B:MATN.0000030974.08984.21