Formal classification of unipotent parameterized diffeomorphisms
arXiv:math/0511298 · doi:10.1017/S0143385707000867
Abstract
We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\cn{n}$ 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 with respect to the regular vector field preserved by . We get invariants specifically attached to higher dimension () although generically they are analogous to the one-dimensional ones.
35 pages