Topological Classification of Holomorphic, Semi-Hyperbolic Germs, in "Quasi-Absence" of Resonances

Abstract

The classification, by topological conjugacy, of invertible holomorphic germs $f:(\mathbb{C}^n,0)\to (\mathbb{C}^n,0)$, with $λ_1,...,λ_n$ eigenvalues of $df_0$, and $|λ_i|\neq 1$ for $i=2,...,n$ while $λ_1$ is a root of the unity, is given, in the suitable hypothesis of ``quasi-absence'' of resonances.