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Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions

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 $Φ$ 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 $N$?
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https://hal-insu.archives-ouvertes.fr/insu-03718990
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Submitted on : Sunday, July 10, 2022 - 11:24:24 AM
Last modification on : Tuesday, August 2, 2022 - 4:32:53 AM

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Alain Chenciner, David Sauzin, Shanzhong Sun, Qiaoling Wei. Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions. Regular and Chaotic Dynamics, 2022, 27, pp.43-64. ⟨10.1134/S1560354722010063⟩. ⟨insu-03718990⟩

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