Alain Chenciner, David Sauzin, Shanzhong Sun, Qiaoling Wei
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Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions
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 \(N\)?
期刊介绍：
Regular and Chaotic Dynamics (RCD) is an international journal publishing original research papers in dynamical systems theory and its applications. Rooted in the Moscow school of mathematics and mechanics, the journal successfully combines classical problems, modern mathematical techniques and breakthroughs in the field. Regular and Chaotic Dynamics welcomes papers that establish original results, characterized by rigorous mathematical settings and proofs, and that also address practical problems. In addition to research papers, the journal publishes review articles, historical and polemical essays, and translations of works by influential scientists of past centuries, previously unavailable in English. Along with regular issues, RCD also publishes special issues devoted to particular topics and events in the world of dynamical systems.
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