# A Proof of Jakobson’s Theorem via Yoccoz puzzles and the measure of stochastic parameters

 Orateur: Mitsuhiro Shishikura Localisation: Université de Kyoto, Japon Type: Séminaire COOL Site: Hors LAMA , IHP Salle: 5 Date de début: 13/09/2013 - 11:15 Date de fin: 13/09/2013 - 11:15

Jakobson's theorem says that a certain family of unimodal maps of the interval has a positive measure set of stochastic'' parameters for which there exist invariant measure absolutely continuous with respect to the Lebesgue measure. Luzzatto-Takahasi gave an effective estimate on the measure, but it was like $10^{-5000}$ for the quadratic family. We will present an alternative approach to Jakobson's theorem using complex extension and Yoccoz puzzle/parapuzzle techniques, and try to improve the estimates on the measure of stochastic parameters.