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- W2093538045 abstract "The purpose of this paper is to study the local behavior of semi-attractive holomorphic self-maps of C (m > 2) in a neighborhood of a fixed point that we assume to be the origin. Such transformations are the ones whose differential at 0 has one eigenvalue equal to 1 while the remaining ones, say β1, . . . , βs with s ≥ 1, have modulus strictly less than 1. Semi-attractive transformations such that 0 is not an isolated fixed point have been studied by Nishimura [N], who considered analytic automorphisms F of complex manifolds admitting a q-dimensional complex submanifoldM of attracting fixed points for F. Then, for each point p0 ∈M, one can choose local coordinates (w, z) ∈ C × Cm−q in a neighborhood U of p0 such that U ∩ M has equation z = 0; hence the map F can be locally written as w1 = w +O(‖z‖), z1 = C(w)z+O(‖z‖2), whereC(w) is a (m−q)× (m−q)matrix whose elements are holomorphic functions onU and whose eigenvalues β1(w), . . . , βm−q(w) have modulus strictly less than 1. Let = {p ∈U | F n(p)→ p0, p0 ∈M}, which is an open set containing M. Nishimura proved that if these eigenvalues have no relations in any point of M, that is, if for each multi-index j = (j1, . . . , jm−q) with∑m−q k=1 jk ≥ 2 and 1≤ i ≤ m− q we have β1 1 (w) · · ·βm−q m−q (w) 6= βi(w), then there exists a biholomorphism S:N → , where π :N → M is the normal bundle of M, which conjugates F to the automorphism G of N induced by F and given in π−1(U ∩M) by s1 = s, u1 = C(s)u." @default.
- W2093538045 created "2016-06-24" @default.
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- W2093538045 date "2001-10-01" @default.
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- W2093538045 title "Parabolic manifolds for semi-attractive holomorphic germs" @default.
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- W2093538045 doi "https://doi.org/10.1307/mmj/1008719770" @default.
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