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Journal Articles Regular and Chaotic Dynamics Year : 2022

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

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Shanzhong Sun
• Function : Author
Qiaoling Wei
• Function : Author

#### 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 $N$?

#### Domains

Sciences of the Universe [physics]

### Dates and versions

insu-03718990 , version 1 (10-07-2022)

### Identifiers

• HAL Id : insu-03718990 , version 1
• ARXIV :
• BIBCODE :
• DOI :

### Cite

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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