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Regular and Chaotic Dynamics, 2022, Volume 27, Issue 1, Pages 43–64
DOI: https://doi.org/10.1134/S1560354722010063 (Mi rcd1152) 		 
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
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DOI: https://doi.org/10.1134/S1560354722010063
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.
Funding agency Grant number
National Natural Science Foundation of China 11771303
12171327
11911530092
11871045
The first two authors thank Capital Normal University for its hospitality. The third author is partially supported by the National Key R&D Program of China (2020YFA0713300), NSFC (Nos. 11771303, 12171327, 11911530092, 11871045).
Received: 15.11.2021
Accepted: 11.01.2022
Bibliographic databases:
Document Type: Article
MSC: 37E30, 37G05
Language: English
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
Citation in format AMSBIB
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\by Alain Chenciner, David Sauzin, Shanzhong Sun, Qiaoling Wei
\paper Elliptic Fixed Points with an Invariant Foliation:
Some Facts and More Questions
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 1
\pages 43--64
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