Voir la notice de l'article provenant de la source Numdam
We study linear and non-linear small divisors problems in analytic and non-analytic regularity. We observe that the Bruno arithmetic condition, which is usually attached to non-linear analytic problems, can also be characterized as the optimal condition to solve the linear problem in some fixed non-quasi-analytic class. Based on this observation, it is natural to conjecture that the optimal arithmetic condition for the linear problem is also optimal for non-linear small divisors problems in any reasonable non-quasi-analytic classes. Our main result proves this conjecture in a representative non-linear problem, which is the linearization of vector fields on the torus, in the most natural non-quasi-analytic class, which is the Gevrey class. The proof follows Moser’s argument of approximation by analytic functions, and uses works of Popov, Rüssmann and Pöschel in an essential way.
@article{AIHPC_2022__39_3_501_0,
author = {Bounemoura, Abed},
title = {Optimal linearization of vector fields on the torus in non-analytic {Gevrey} classes},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {501--528},
volume = {39},
number = {3},
year = {2022},
doi = {10.4171/aihpc/12},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4171/aihpc/12/}
}
TY - JOUR AU - Bounemoura, Abed TI - Optimal linearization of vector fields on the torus in non-analytic Gevrey classes JO - Annales de l'I.H.P. Analyse non linéaire PY - 2022 SP - 501 EP - 528 VL - 39 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4171/aihpc/12/ DO - 10.4171/aihpc/12 LA - en ID - AIHPC_2022__39_3_501_0 ER -
%0 Journal Article %A Bounemoura, Abed %T Optimal linearization of vector fields on the torus in non-analytic Gevrey classes %J Annales de l'I.H.P. Analyse non linéaire %D 2022 %P 501-528 %V 39 %N 3 %U http://geodesic.mathdoc.fr/articles/10.4171/aihpc/12/ %R 10.4171/aihpc/12 %G en %F AIHPC_2022__39_3_501_0
Bounemoura, Abed. Optimal linearization of vector fields on the torus in non-analytic Gevrey classes. Annales de l'I.H.P. Analyse non linéaire, Tome 39 (2022) no. 3, pp. 501-528. doi: 10.4171/aihpc/12
Cité par Sources :