On convergent normal from transformations in presence of symmetries (Q1973941)

The author proves a convergence criterion for transformations to (Poincaré-Dulac) normal form, which is a generalization of a theorem on the convergence of normalizing transformations in the presence of symmetries due to \textit{G. Cicogna} [J. Math. Anal. Appl. 199, No. 1, 243-255 (1996; Zbl 0855.34042)]. This last theorem extends results of \textit{L. M. Markhashov} [J. Appl. Math. Mech. 38, 738-740 (1975; Zbl 0359.34006)] and \textit{A. D. Bruno} and \textit{S. Walcher} [J. Math. Anal. Appl. 183, No. 3, 571-576 (1994; Zbl 0804.34040)]. On the other hand, the author also shows that the imposed technical hypotheses allow to carry out a computational verification in several classes of vector fields.