%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