%0 Journal Article
%T Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions
%+ Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE)
%A Chenciner, Alain
%A Sauzin, David
%A Sun, Shanzhong
%A Wei, Qiaoling
%< avec comité de lecture
%@ 1560-3547
%J Regular and Chaotic Dynamics
%I MAIK Nauka/Interperiodica
%V 27
%P 43-64
%8 2022
%D 2022
%Z 2111.07714
%Z 2022RCD....27...43C
%R 10.1134/S1560354722010063
%K normal form
%K Arnold family
%K weakly attracting fixed point
%K Mathematics - Dynamical Systems
%K 37E30 (Primary) 37G05 (Secondary)
%Z Sciences of the Universe [physics]Journal articles
%X We address the following question: let $F:(\mathbb{R}2,0)\to(\mathbb{R}2,0)$ be an analytic local diffeomorphism defined in the neighborhood of the nonresonant elliptic fixed point 0 and let $Φ$ be a formal conjugacy to a normal form $N$. Supposing $F$ leaves invariant the foliation by circles centered at $0$, what is the analytic nature of $Φ$ and $N$?
%G English
%L insu-03718990
%U https://insu.hal.science/insu-03718990
%~ OBSPM
%~ INSU
%~ CNRS
%~ IMCCE
%~ PSL
%~ UNIV-LILLE
%~ SORBONNE-UNIVERSITE
%~ SORBONNE-UNIV
%~ SU-SCIENCES
%~ OBSPM-PSL
%~ SU-TI
%~ ALLIANCE-SU