The boundary of bounded polynomial Fatou components

Pascale Roesch; Yongcheng Yin

doi:10.1016/j.crma.2008.06.004

Dynamical Systems

The boundary of bounded polynomial Fatou components

Presented by: Étienne Ghys

Pascale Roesch ¹; Yongcheng Yin ²

¹ Laboratoire Émile-Picard, Université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 9, France
² School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 877-880.

Abstract
Résumé

We prove that, for a polynomial, every bounded Fatou component, with the exception of Siegel disks, has for boundary a Jordan curve.

Nous montrons que le bord de toute composante de Fatou bornée d' un polynôme, hormis les disques de Siegel, est une courbe de Jordan.

Received: 2007-12-24
Accepted: 2008-06-11
Published online: 2008-07-07

DOI: 10.1016/j.crma.2008.06.004

Author's affiliations:

Pascale Roesch ¹; Yongcheng Yin ²

¹ Laboratoire Émile-Picard, Université Paul-Sabatier, 118, route de Narbonne, 31062 Toulouse cedex 9, France
² School of Mathematical Sciences, Fudan University, Shanghai, 200433, China

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     title = {The boundary of bounded polynomial {Fatou} components},
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     language = {en},
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Pascale Roesch; Yongcheng Yin. The boundary of bounded polynomial Fatou components. Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 877-880. doi : 10.1016/j.crma.2008.06.004. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.06.004/

References
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[5] W. Qiu; Y. Yin Proof of the Branner–Hubbard conjecture on Cantor Julia sets (preprint) | arXiv

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