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.
Articolo in rivista - Articolo scientifico
Linearization, Resonances, Brjuno condition, Discrete local holomorphic dynamical systems
English
881
900
Raissy, J. (2009). Linearization of holomorphic germs with quasi-Brjuno fixed points. MATHEMATISCHE ZEITSCHRIFT, 264(4), 881-900 [10.1007/s00209-009-0493-z].
Raissy, J
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/8672
Citazioni
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
Social impact