Dynamics of quadratic polynomials: complex bounds for real maps
Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1219-1255.

Nous démontrons des bornes complexes pour les applications quadratiques réelles infiniment renormalisables dont la combinatoire est essentiellement bornée. C’est le dernier ingrédient manquant dans le problème des bornes complexes pour les applications quadratiques réelles infiniment renormalisables. Un de des corollaires est que l’ensemble de Julia de toute application quadratique réelle z↦z 2 +c,c∈[-2,1/4] est localement connexe.

We prove complex bounds for infinitely renormalizable real quadratic maps with essentially bounded combinatorics. This is the last missing ingredient in the problem of complex bounds for all infinitely renormalizable real quadratics. One of the corollaries is that the Julia set of any real quadratic map z↦z 2 +c, c∈[-2,1/4], is locally connected.

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     title = {Dynamics of quadratic polynomials: complex bounds for real maps},
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Lyubich, Mikhail; Yampolsky, Michael. Dynamics of quadratic polynomials: complex bounds for real maps. Annales de l'Institut Fourier, Tome 47 (1997) no. 4, pp. 1219-1255. doi : 10.5802/aif.1598. http://www.numdam.org/articles/10.5802/aif.1598/

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