American Journal of Mathematics

We shall describe a canonical procedure to associate to any (germ of) holomorphic self-map F of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]ⁿ fixing the origin so that dF_O is invertible and nondiagonalizable an n-dimensional complex manifold M, a holomorphic map π: M → [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /]ⁿ, a point e ∈ M and a (germ of) holomorphic self-map [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /] of M such that: π restricted to M\π^-1(O is a biholomorphism between M\π^-1(O) and [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="04i" /]ⁿ\{O}; π ○ [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="05i" /] = F ○ π; and e is a fixed point of [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="06i" /] such that [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="07i" /] is diagonalizable. Furthermore, we shall use this construction to describe the local dynamics of such an F nearby the origin when sp (dF_O) = {1}.