Formal classification of unipotent parameterized diffeomorphisms

We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\text{cn}n$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a linear differential equation. Then we describe the formal invariants; their nature depends on the position of the fixed points set $Fix \phi$withrespecttotheregularvectorfieldpreservedby$\phi$. We get invariants specifically attached to higher dimension ($n\ge 3$) although generically they are analogous to the one-dimensional ones.