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

Type:
Type:
Site:
Date:
13/09/2013 - 11:15
Salle:
05
Orateur:
Mitsuhiro Shishikura
Localisation:
Université de Kyoto
Localisation:
Japon
Résumé:

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.
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