Geodesic
Local invariants of differential equations
Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 499-507

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider an analytic system $X=\Phi(X)$ in the neighborhood of the fixed point $X=0$. Depending on the characteristic numbers of the matrix $(\partial\Phi/\partial X)_0$, we define the integer $d\ge0$ as the ldquodimensionrdquo of the normal form or as the ldquomultiplicityrdquo of the resonance. We show that a system with $d=1$, subject to certain additional assumptions, has a finite number of invariants relative to reversible formal changes of variables $X=\Xi(Y)$. All these invariants are the coefficients of some normal form. We touch upon questions concerning invariants of relatively smooth and continuous substitutions. 
@article{MZM_1973_14_4_a5,
     author = {A. D. Bruno},
     title = {Local invariants of differential equations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {499--507},
     publisher = {mathdoc},
     volume = {14},
     number = {4},
     year = {1973},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a5/}
}
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A. D. Bruno. Local invariants of differential equations. Matematičeskie zametki, Tome 14 (1973) no. 4, pp. 499-507. http://geodesic.mathdoc.fr/item/MZM_1973_14_4_a5/