Formal classification of unipotent parameterized diffeomorphisms
Javier Ribón
Abstract
We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at 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 ϕ with respect to the regular vector field preserved by ϕ. We get invariants specifically attached to higher dimension (n ≥ 3) although generically they are analogous to the one-dimensional ones.
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