Tue, 15 Nov 2005
DH 3rd floor SR
Dr Stefano Luzzatto

We formulate and prove a Jakobson-Benedicks-Carleson type theorem on the occurrence of nonuniform hyperbolicity (stochastic dynamics) in families of one-dimensional maps, based on computable starting conditions and providing explicit, computable, lower bounds for the measure of the set of selected parameters. As a first application of our results we obtain a first ever explicit lower bound for the set of parameters corresponding to maps in the quadratic family f_{a}(x) = x^{2}-a which have an absolutely continuous invariant probability measure.

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