Geodesic
On New Resonances and Normal Forms of Autonomous Systems with One Zero Eigenvalue
Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 63-77

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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 study the reducibility of such systems to polynomial normal form.
Keywords: autonomous system, ordinary differential equations, singular point, zero eigenvalue, Taylor series, resonance
Mots-clés : polynomial normal form. 
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     author = {V. S. Samovol},
     title = {On {New} {Resonances} and {Normal} {Forms} of {Autonomous} {Systems} with {One} {Zero} {Eigenvalue}},
     journal = {Matemati\v{c}eskie zametki},
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     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a5/}
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V. S. Samovol. On New Resonances and Normal Forms of Autonomous Systems with One Zero Eigenvalue. Matematičeskie zametki, Tome 88 (2010) no. 1, pp. 63-77. http://geodesic.mathdoc.fr/item/MZM_2010_88_1_a5/