Comptes Rendus
no. 15-16
Dynamical Systems
The boundary of bounded polynomial Fatou components
[Frontière des composantes de Fatou polynômiales]

Présenté par : Étienne Ghys

Pascale Roesch1 ; Yongcheng Yin2
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.

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

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

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.06.004
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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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/

[1] J. Kahn, M. Lyubich, The quasi-additivity law in conformal geometry, Ann. of Math., in press

[2] J. Kiwi Real laminations and the topological dynamics of complex polynomials, Adv. Math., Volume 184 (2004), pp. 207-267

[3] O. Kozlovski; W. Shen; S. van Strien Rigidity for real polynomials, Ann. of Math., Volume 165 (2007), pp. 749-841

[4] C.L. Petersen, P. Roesch, Parabotools, manuscript

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

[6] P. Roesch Cubic polynomials with a parabolic point (preprint) | arXiv

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