Exponentially long time stability for non-linearizable analytic germs of ( ℂ n , 0 ) .

Timoteo Carletti[1]

  • [1] Scuola Normale Superiore, piazza dei Cavalieri 7, 56126 Pisa (Italie)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 4, page 989-1004
  • ISSN: 0373-0956

Abstract

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We study the Siegel-Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey- s , s > 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- s 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.

How to cite

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Carletti, Timoteo. "Exponentially long time stability for non-linearizable analytic germs of $({\mathbb {C}}^n,0)$.." Annales de l’institut Fourier 54.4 (2004): 989-1004. <http://eudml.org/doc/116139>.

@article{Carletti2004,
abstract = {We study the Siegel-Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey-$s$, $s&gt;0$ 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-$s$ 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.},
affiliation = {Scuola Normale Superiore, piazza dei Cavalieri 7, 56126 Pisa (Italie)},
author = {Carletti, Timoteo},
journal = {Annales de l’institut Fourier},
keywords = {Siegel center problem; Gevrey class; Bruno condition; effective stability; Nekoroshev like estimates; Nekoroshev-like estimates},
language = {eng},
number = {4},
pages = {989-1004},
publisher = {Association des Annales de l'Institut Fourier},
title = {Exponentially long time stability for non-linearizable analytic germs of $(\{\mathbb \{C\}\}^n,0)$.},
url = {http://eudml.org/doc/116139},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Carletti, Timoteo
TI - Exponentially long time stability for non-linearizable analytic germs of $({\mathbb {C}}^n,0)$.
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 4
SP - 989
EP - 1004
AB - We study the Siegel-Schröder center problem on the linearization of analytic germs of diffeomorphisms in several complex variables, in the Gevrey-$s$, $s&gt;0$ 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-$s$ 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.
LA - eng
KW - Siegel center problem; Gevrey class; Bruno condition; effective stability; Nekoroshev like estimates; Nekoroshev-like estimates
UR - http://eudml.org/doc/116139
ER -

References

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