Phase-parameter relation and sharp statistical properties for general families of unimodal maps
| dc.creator | Avila, Artur | |
| dc.creator | Moreira, Carlos Gustavo | |
| dc.date | 2003-06-10 | |
| dc.date.accessioned | 2026-07-07T04:58:42Z | |
| dc.date.available | 2026-07-07T04:58:42Z | |
| dc.description | We obtain estimates relating the phase space and the parameter space of analytic families of unimodal maps. Using those estimates, we show that typical analytic unimodal maps admit a quasiquadratic renormalization. This reduces the study of the statistical properties of typical unimodal maps to the quasiquadratic case which had been studied in \cite {AM2}. The estimates proved here correspond exactly to the Phase-Parameter relation proved in \cite {AM} in the quadratic case, and allows one to obtain sharp estimates on the dynamics of typical unimodal maps which were available only in the quadratic case: as an example we conclude that the exponent of the polynomial recurrence of the critical orbit is exactly one. We also show that those ideas lead to a new proof of a Theorem of Shishikura: the set of non-renormalizable parameters in the boundary of the Mandelbrot set has Lebesgue measure zero. Further applications of those results can be found in the companion paper \cite {AM3}. | |
| dc.description | 40 pages, no figures, first version | |
| dc.identifier | https://arxiv.org/abs/math/0306156 | |
| dc.identifier | http://arxiv.org/abs/math/0306156 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67748 | |
| dc.subject | Dynamical Systems | |
| dc.title | Phase-parameter relation and sharp statistical properties for general families of unimodal maps | |
| dc.type | text |