Parapuzzle of the multibrot set and typical dynamics of unimodal maps
Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 27-56
Cet article a éte moissonné depuis la source EMS Press
We study the parameter space of unicritical polynomials fc:z↦zd+c. For complex parameters, we prove that for Lebesgue almost every c, the map fc is either hyperbolic or infinitely renormalizable. For real parameters, we prove that for Lebesgue almost every c, the map fc is either hyperbolic, or Collet–Eckmann, or infinitely renormalizable. These results are based on controlling the spacing between consecutive elements in the “principal nest” of parapuzzle pieces.
@article{JEMS_2011_13_1_a1,
author = {Artur Avila and Mikhail Lyubich and Weixiao Shen},
title = {Parapuzzle of the multibrot set and typical dynamics of unimodal maps},
journal = {Journal of the European Mathematical Society},
pages = {27--56},
year = {2011},
volume = {13},
number = {1},
doi = {10.4171/jems/243},
url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/243/}
}
TY - JOUR AU - Artur Avila AU - Mikhail Lyubich AU - Weixiao Shen TI - Parapuzzle of the multibrot set and typical dynamics of unimodal maps JO - Journal of the European Mathematical Society PY - 2011 SP - 27 EP - 56 VL - 13 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4171/jems/243/ DO - 10.4171/jems/243 ID - JEMS_2011_13_1_a1 ER -
%0 Journal Article %A Artur Avila %A Mikhail Lyubich %A Weixiao Shen %T Parapuzzle of the multibrot set and typical dynamics of unimodal maps %J Journal of the European Mathematical Society %D 2011 %P 27-56 %V 13 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4171/jems/243/ %R 10.4171/jems/243 %F JEMS_2011_13_1_a1
Artur Avila; Mikhail Lyubich; Weixiao Shen. Parapuzzle of the multibrot set and typical dynamics of unimodal maps. Journal of the European Mathematical Society, Tome 13 (2011) no. 1, pp. 27-56. doi: 10.4171/jems/243
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