Linearization of holomorphic germs with quasi-Brjuno fixed points

Details Linearization of holomorphic germs with quasi-Brjuno fixed points Linearization of holomorphic germs with quasi-Brjuno fixed points

2007-10-19

arxiv.org/abs/0710.3650v3

Mathematics

Dynamical Systems

20 pages; added some statements and an example to clarify the context

Scientific paper

10.1007/s00209-009-0493-z

Let $f$ be a germ of holomorphic diffeomorphism of $\C^n$ 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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