Geodesic
Finitely Smooth Local Equivalence of Autonomous Systems with One Zero Root
Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 275-287 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, in a neighborhood of a singular point, we consider autonomous systems of ordinary differential equations such that the matrix of their linear part has one zero eigenvalue, while the other eigenvalues lie outside the imaginary axis. We prove that the problem of finitely smooth equivalence can be solved for such systems by using finite segments of the Taylor series of their right-hand sides.
Keywords: autonomous system, ordinary differential equations, finitely smooth equivalence, singular point, zero eigenvalue, Taylor series, normal form, $N$-jet of a function. 
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V. S. Samovol. Finitely Smooth Local Equivalence of Autonomous Systems with One Zero Root. Matematičeskie zametki, Tome 88 (2010) no. 2, pp. 275-287. http://geodesic.mathdoc.fr/item/MZM_2010_88_2_a9/

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