Let f be a germ of holomorphic diffeomorphism of $${\mathbb {C}^{n}}$$ fixing the origin O, with df_O diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of df_O and some restrictions on the resonances, f is locally holomorphically linearizable if and only if there exists a particular f-invariant complex manifold. Most of the classical linearization results can be obtained as corollaries of our result.
Raissy, J. (2009). Linearization of holomorphic germs with quasi-Brjuno fixed points. MATHEMATISCHE ZEITSCHRIFT, 264(4), 881-900 [10.1007/s00209-009-0493-z].
Linearization of holomorphic germs with quasi-Brjuno fixed points
RAISSY, JASMIN
2009
Abstract
Let f be a germ of holomorphic diffeomorphism of $${\mathbb {C}^{n}}$$ fixing the origin O, with df_O diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of df_O and some restrictions on the resonances, f is locally holomorphically linearizable if and only if there exists a particular f-invariant complex manifold. Most of the classical linearization results can be obtained as corollaries of our result.
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