We introduce the notion of (n,d)-sets and show several Noguchi-type convergence-extension theorems for (n,d)-sets.

The formal class of a germ of diffeomorphism $\varphi$ is embeddable in a flow if $\varphi$ is formally conjugated to the exponential of a germ of vector field. We prove that there are complex analytic unipotent germs of diffeomorphisms at ${ℂ}^n$ ($n\>1$) whose formal class is non-embeddable. The examples are inside a family in which the non-embeddability is of geometrical type. The proof relies on the properties of some linear functional operators that we obtain through the study of polynomial families of diffeomorphisms...