Normal form for maps with nilpotent linear part

The normal form for an n -dimensional map with irreducible nilpotent linear part is determined using s mathvariant="fraktur">l 2 -representation theory. We sketch by example how the reducible case can also be treated in algorithmic manner. construction (and proof) of -triple from more complicated than one would hope for, but once abstract theory place, both description and computational splitting to compute generator coordinate transformation handled explicitly terms without explicit knowledge triple. If wishes such that it guaranteed lie kernel operator sure this really a respect part; state -style. Although at first sight maps vector fields case, turns out final result much better. Where field runs into invariant theoretical problems when dimension gets larger if wants describe general form, we obtain results any restrictions on dimension. In literature only two-dimensional has been described so far, as far know.