Wednesday, December 12, 2012

Statistical stability for Lorenz attractors

Mohammad Soufi
(Universidade do Porto)

Abstract: In this talk we consider the robust family of Lorenz attractors. These attractors are chaotic in the sense that they are transitive and have sensitive dependence on the initial conditions. Moreover, they support SRB measures. We show that the SRB measures depend continuously on the dynamics in the weak∗ topology. In other words, the Lorenz attractors are statistical stable. We also consider a one parameter family with positive Lebesgue measure of one-dimensional maps arising from the contracting Lorenz attractors studied by Rovella. Benedicks-Carleson technique was used by Rovella to prove the existence of this family of maps and also the exponential grows of their derivatives along their critical orbits whose recurrences to the critical point are slow. Here we use the technique developed by Freitas to show that the tail set (the set of points which at a given time have not achieved either the exponential growth of derivative or the slow recurrence) decays exponentially fast as time passes. As a consequence, we obtain the existence of an SRB measure for each map in the family, and the continuous variation of the densities of the SRB measures and associated metric entropies with the parameter.

Wednesday, December 12, 2012
Time: 16h00
Room: Sala IAPMEI, Edificio Quelhas, ISEG