Linearisation par diffeomorphisme et immersion des systemes

In this paper we show that the linearization of a nonlinear dynamics via coordinate transformations is in fact a particular case of a linearization by "immersion" which was introduced recently (D. Claude, M. Fliess, A. Isidori, C.R. Acad. Sc. Paris, 296, Serie I, 1983). We establish that the linearization by diffeomorphism is related directly to the "characteristic numbers" also known as "differential indices" that are used in nonlinear decoupling too.