%0 Journal Article
%T Parapuzzle of the Multibrot set and typical dynamics of unimodal maps
%A Artur Avila
%A Mikhail Lyubich
%A Weixiao Shen
%J Mathematics
%D 2008
%I arXiv
%X We study the parameter space of unicritical polynomials $f_c:z\mapsto z^d+c$. For complex parameters, we prove that for Lebesgue almost every $c$, the map $f_c$ is either hyperbolic or infinitely renormalizable. For real parameters, we prove that for Lebesgue almost every $c$, the map $f_c$ 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.
%U http://arxiv.org/abs/0804.2197v1