In this paper, we show a way to characterize the R-automorphisms of formal power series on several indeterminates and with coefficients over a commutative ring with identity, R. We show this characterization, as an extension of existing result for the R-automorphisms of the formal power series in an indeterminate, given by O’Malley, M. and Wood, C. in [12].

In this paper, we resolve the problem of finding a formal change of coordinates between formal vector field and another more simple (its «canonical form»}. In particular, we proof the Poincaré's theorem of formal linearization and the Poincaré-Dulac theorem.

In this paper, we resolve the problem of finding a formal change of coordinates between formal vector field and another more simple (its «canonical form»}. In particular, we proof the Poincaré's theorem of formal linearization and the Poincaré-Dulac theorem.