Geodesic
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.

Voir la notice de l'article provenant de 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.
DOI : 10.4171/jems/243
Classification : 37-XX, 16-XX, 00-XX 
@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},
     publisher = {mathdoc},
     volume = {13},
     number = {1},
     year = {2011},
     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
PB  - mathdoc
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
%I mathdoc
%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. http://geodesic.mathdoc.fr/articles/10.4171/jems/243/

Cité par Sources :