Geodesic
Normal form of real differential equations
Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 227-241 Cet article a éte moissonné depuis la source Math-Net.Ru

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In a neighborhood of a fixed point we consider an autonomous analytic system of ordinary differential equations. We establish the existence of a normalizing transformation for which the normal form retains the properties of the original system such as reality and invariance with respect to a linear change of variables. For real systems we consider the problem of existence of an analytic transformation into normal form and the problem of existence of a finitely smooth transformation into a linear system. 
@article{MZM_1975_18_2_a8,
     author = {A. D. Bruno},
     title = {Normal form of real differential equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {227--241},
     year = {1975},
     volume = {18},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a8/}
}
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A. D. Bruno. Normal form of real differential equations. Matematičeskie zametki, Tome 18 (1975) no. 2, pp. 227-241. http://geodesic.mathdoc.fr/item/MZM_1975_18_2_a8/