Dynamical Systems
The boundary of bounded polynomial Fatou components
Comptes Rendus. Mathématique, Volume 346 (2008) no. 15-16, pp. 877-880.

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:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.06.004
Roesch, Pascale 1; Yin, Yongcheng 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
@article{CRMATH_2008__346_15-16_877_0,
     author = {Roesch, Pascale and Yin, Yongcheng},
     title = {The boundary of bounded polynomial {Fatou} components},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {877--880},
     publisher = {Elsevier},
     volume = {346},
     number = {15-16},
     year = {2008},
     doi = {10.1016/j.crma.2008.06.004},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/j.crma.2008.06.004/}
}
TY  - JOUR
AU  - Roesch, Pascale
AU  - Yin, Yongcheng
TI  - The boundary of bounded polynomial Fatou components
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 877
EP  - 880
VL  - 346
IS  - 15-16
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/j.crma.2008.06.004/
DO  - 10.1016/j.crma.2008.06.004
LA  - en
ID  - CRMATH_2008__346_15-16_877_0
ER  - 
%0 Journal Article
%A Roesch, Pascale
%A Yin, Yongcheng
%T The boundary of bounded polynomial Fatou components
%J Comptes Rendus. Mathématique
%D 2008
%P 877-880
%V 346
%N 15-16
%I Elsevier
%U http://www.numdam.org/articles/10.1016/j.crma.2008.06.004/
%R 10.1016/j.crma.2008.06.004
%G en
%F CRMATH_2008__346_15-16_877_0
Roesch, Pascale; Yin, Yongcheng. 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. http://www.numdam.org/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] Kiwi, J. Real laminations and the topological dynamics of complex polynomials, Adv. Math., Volume 184 (2004), pp. 207-267

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

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

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

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

Cited by Sources: