Geodesic
Normal Form of Autonomous Systems with One Zero Eigenvalue
Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 711-720

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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. 
@article{MZM_2004_75_5_a7,
     author = {V. S. Samovol},
     title = {Normal {Form} of {Autonomous} {Systems} with {One} {Zero} {Eigenvalue}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {711--720},
     publisher = {mathdoc},
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     number = {5},
     year = {2004},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a7/}
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V. S. Samovol. Normal Form of Autonomous Systems with One Zero Eigenvalue. Matematičeskie zametki, Tome 75 (2004) no. 5, pp. 711-720. http://geodesic.mathdoc.fr/item/MZM_2004_75_5_a7/