Geodesic
Combinatorial rigidity for unicritical polynomials
Artur Avila1 ; Jeremy Kahn2 ; Mikhail Lyubich3 ; Weixiao Shen4
1 CNRS UMR 7599<br/>Laboratoire de Probabilités et Modèles<br/>Aléatoires<br/>Université Pierre et Marie Curie<br/>Boîte courrier 188<br/>75252 Paris Cedex 05<br/>France
2 Department of Mathematics<br/>Stony Brook University<br/>Stony Brook, NY 11794-3651<br/>United States
3 Department of Mathematics<br/>University of Toronto<br/>Room 6290, 40 St. George Street<br/>Toronto, ON M5S 2E4<br/>Canada
4 Department of Mathematics<br/>National University of Singapore<br/>2, Science Drive 2<br/>Singapore 117543
Annals of mathematics, Tome 170 (2009) no. 2, pp. 783-797

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove that any unicritical polynomial $f_c:z\mapsto z^d+c$ which is at most finitely renormalizable and has only repelling periodic points is combinatorially rigid. This implies that the connectedness locus (the “Multibrot set”) is locally connected at the corresponding parameter values and generalizes Yoccoz’s Theorem for quadratics to the higher degree case.

DOI : 10.4007/annals.2009.170.783

Artur Avila 1 ; Jeremy Kahn 2 ; Mikhail Lyubich 3 ; Weixiao Shen 4

1 CNRS UMR 7599<br/>Laboratoire de Probabilités et Modèles<br/>Aléatoires<br/>Université Pierre et Marie Curie<br/>Boîte courrier 188<br/>75252 Paris Cedex 05<br/>France
2 Department of Mathematics<br/>Stony Brook University<br/>Stony Brook, NY 11794-3651<br/>United States
3 Department of Mathematics<br/>University of Toronto<br/>Room 6290, 40 St. George Street<br/>Toronto, ON M5S 2E4<br/>Canada
4 Department of Mathematics<br/>National University of Singapore<br/>2, Science Drive 2<br/>Singapore 117543 
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Artur Avila; Jeremy Kahn; Mikhail Lyubich; Weixiao Shen. Combinatorial rigidity for unicritical polynomials. Annals of mathematics, Tome 170 (2009) no. 2, pp. 783-797. doi: 10.4007/annals.2009.170.783

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