Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Linearization of holomorphic germs with quasi-Brjuno fixed points

Linearization of holomorphic germs with quasi-Brjuno fixed points 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Linearization of holomorphic germs with quasi-Brjuno fixed points

Mathematische Zeitschrift , Volume 264 (4): 20 – Apr 1, 2010

Loading next page...
 
/lp/springer-journals/linearization-of-holomorphic-germs-with-quasi-brjuno-fixed-points-hVhNIO0jhh

References (23)

Publisher
Springer Journals
Copyright
2009 Springer-Verlag
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-009-0493-z
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Apr 1, 2010

There are no references for this article.