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**Example text**

N be the eigenvalues of the linear part. We say that F is oneresonant with respect to the Àrst m eigenvalues {λ1 , . . , λm } (1 ≤ m ≤ n) (or partially one-resonant) if there exists a Àxed multi-index α = (α1 , . . , αm , 0, . . , 0) = 0 ∈ Nn such that for s ≤ m, the resonances βj kα j n m λs = j=1 λ j are precisely of the form λs = λs j=1 λ j , where k ≥ 1 ∈ N is arbitrary. This notion has been introduced in [12]. The main advantage of such a notion of partial one-resonance is that it can be applied to the subset of all eigenvalues of modulus equal to 1, regardless of the relations which might occur among the other eigenvalues.

B RACCI and F. T OVENA , Embeddings of submanifolds and normal bundles, Adv. Math. 220 (2009), 620–656. [6] M. A BATE and F. 3485 (2009). [7] V. I. A RNOLD, “Geometrical Methods in the Theory of Ordinary Differential Equations, Springer, 1983. [8] F. B RACCI, Local dynamics of holomorphic diffeomorphisms, Boll. UMI 7-B (8) (2004), 609–636. [9] F. B RACCI, Local holomorphic dynamics of diffeomorphisms in dimension one, Contemporary Mathematics 525 (2010), 1–42. [10] F. B RACCI and L. M OLINO, The dynamics near quasi-parabolic Àxed points of holomorphic diffeomorphisms in C2 , Amer.

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