Parapuzzle of the Multibrot set and typical dynamics of unimodal maps
| dc.creator | Avila, Artur | |
| dc.creator | Lyubich, Mikhail | |
| dc.creator | Shen, Weixiao | |
| dc.date | 2008-04-14 | |
| dc.date.accessioned | 2026-07-07T09:32:15Z | |
| dc.date.available | 2026-07-07T09:32:15Z | |
| dc.description | 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. | |
| dc.identifier | https://arxiv.org/abs/0804.2197 | |
| dc.identifier | http://arxiv.org/abs/0804.2197 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/158747 | |
| dc.subject | Dynamical Systems | |
| dc.title | Parapuzzle of the Multibrot set and typical dynamics of unimodal maps | |
| dc.type | text |