Georgi Chakvetadze (Moscow U. and Hebrew U.)

will speak on

Random parameter perturbations of Collet-Eckmann maps of the interval.

Abstract:

Continuing the line of research carried out by Baladi, Benedicks, Katok, Kifer, Viana, Young and others we prove that many quadratic maps are strongly stochastically stable with respect to the random parameter perturbations. This means that for a positive Lebesgue measure set in the parameter space the corresponding quadratic map possesses a unique normalized invariant density which remains almost the same in $L_1$-metric if we add small random noise to the map assuming that randomness is in its parameter (in the normalization x|--->\lambda x(1-x)).

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Last update on 20/10/02.