Topological Classification of Holomorphic, Semi-Hyperbolic Germs, in   "Quasi-Absence" of Resonances
  The classification, by topological conjugacy, of invertible holomorphic germs $f:(\mathbb{C}^n,0)\to (\mathbb{C}^n,0)$, with $\lambda_1,...,\lambda_n$ eigenvalues of $df_0$, and $|\lambda_i|\neq 1$ for $i=2,...,n$ while $\lambda_1$ is a root of the unity, is given, in the suitable hypothesis of ``quasi-absence'' of resonances. 
Pietro Di Giuseppe