English

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--ss, s>0s>0 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--ss 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

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