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We establish a Poincaré-Dulac theorem for sequences ${\left(G_n\right)}_{n\in \mathbb{Z}}$ of holomorphic contractions whose differentials $d_0{G}_n$ split regularly. The resonant relations determining the normal forms hold on the moduli of the exponential rates of contraction. Our results are actually stated in the framework of bundle maps. Such sequences of holomorphic contractions appear naturally as iterated inverse branches of endomorphisms of $ℂ{\mathbb{P}}^k$. In this context, our normalization result allows to estimate precisely the distortions...