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The formal class of a germ of diffeomorphism $\phi$ is embeddable in a flowif $\phi$ is formally conjugated to the exponential of a germ of vector field.We prove that there are complex analytic unipotent germs of diffeomorphisms at$({\mathbb C}^{n},0)$ ($n>1$) whose formal class is non-embeddable. Theexamples are inside a family in which the non-embeddability is of geometricaltype. The proof relies on the properties of some linear functional operatorsthat we obtain through the study of polynomial families of diffeomorphisms viapotential theory.

Non-embeddability of general unipotent diffeomorphisms up to formal conjugacy