Geodesic
On local connectivity for the Julia set of rational maps: Newton’s famous example
Pascale Roesch1
1 Le Département de Mathématiques<br/>Université Toulouse 1 Sciences Sociales<br/>31042 Toulouse<br/>France
Annals of mathematics, Tome 168 (2008) no. 1, pp. 127-174.

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

We show that Newton’s cubic methods (famous rational maps) have a locally connected Julia set except in some very specific cases. In particular, when those maps are infinitely renormalizable their Julia set is locally connected and contains small copies of nonlocally connected quadratic Julia sets. This also holds when Newton’s method is renormalizable and has Cremer points, unlike the polynomial case. After a dynamical description we show the necessity of the Brjuno condition within this family.
DOI : 10.4007/annals.2008.168.127

Pascale Roesch 1

1 Le Département de Mathématiques<br/>Université Toulouse 1 Sciences Sociales<br/>31042 Toulouse<br/>France 
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Pascale Roesch. On local connectivity for the Julia set of rational maps: Newton’s famous example. Annals of mathematics, Tome 168 (2008) no. 1, pp. 127-174. doi : 10.4007/annals.2008.168.127. http://geodesic.mathdoc.fr/articles/10.4007/annals.2008.168.127/

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