Exponentially long time stability for non--linearizable analytic germs of $(\C^n,0)$
Dynamical Systems
2007-05-23 v1 Complex Variables
Abstract
We study the Siegel--Schr\"oder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey--, category. We introduce a new arithmetical condition of Bruno type on the linear part of the given germ, which ensures the existence of a Gevrey-- formal linearization. We use this fact to prove the effective stability, i.e. stability for finite but long time, of neighborhoods of the origin for the analytic germ.
Keywords
Cite
@article{arxiv.math/0207006,
title = {Exponentially long time stability for non--linearizable analytic germs of $(\C^n,0)$},
author = {Timoteo Carletti},
journal= {arXiv preprint arXiv:math/0207006},
year = {2007}
}
Comments
10 pages