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

  title={Elliptic Fixed Points with an Invariant Foliation: Some Facts and More Questions},
  author={Alain Chenciner and David Sauzin and Shanzhong Sun and Qiaoling Wei},
  journal={Regular and Chaotic Dynamics},
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 $$N$$ ? 



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© Société mathématique de France, 1992, tous droits réservés. L’accès aux archives de la collection « Astérisque » (http://smf4.emath.fr/ Publications/Asterisque/) implique l’accord avec les

Mapping the circle onto itself

  • (Russian), Izv. Akad. Nauk SSSR Ser. Mat
  • 1961

Small denominators. I. Mapping the circle onto itself

  • Russian)