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Abstract Let f be a germ of holomorphic diffeomorphism of \({\mathbb {C}^{n}}\) fixing the origin O, with d f O diagonalizable. We prove that, under certain arithmetic conditions on the eigenvalues of d f 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.
Mathematische Zeitschrift – Springer Journals
Published: Apr 1, 2010
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