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Elliptic Fixed Points with an Invariant Foliation:
Some Facts and More Questions
Alain Chencinerab, David Sauzinb, Shanzhong Suncd, Qiaoling Weic a University Paris 7, F75014 Paris, France
b IMCCE, Observatoire de Paris, PSL Research University, CNRS,
av. Denfert-Rochereau 77, 75014 Paris, France
c School of Mathematical Sciences, Capital Normal University
d Academy for Multidisciplinary Studies, Capital Normal University,
100048 Beijing, China
Abstract:
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 $\Phi$ 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 $\Phi$ and $N$?
Keywords:
normal form, Arnold family, weakly attracting fixed point.
Received: 15.11.2021 Accepted: 11.01.2022
Citation:
Alain Chenciner, David Sauzin, Shanzhong Sun, Qiaoling Wei, “Elliptic Fixed Points with an Invariant Foliation:
Some Facts and More Questions”, Regul. Chaotic Dyn., 27:1 (2022), 43–64
Linking options:
https://www.mathnet.ru/eng/rcd1152 https://www.mathnet.ru/eng/rcd/v27/i1/p43
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