Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions
Résumé
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 $N$?