Linear response for random dynamical systems

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Date(s) - 19/12/2017
11 h 00 min - 12 h 00 min


We study for the first time linear response for random compositions of maps, chosen independently according to a distribution ℙ. We are interested in the following question: how does an absolutely continuous stationary measure (acsm) of a random system change when ℙ changes smoothly to ℙε? For a wide class of one-dimensional random maps, we prove differentiability of acsm with respect to ε; moreover, we obtain a linear-response formula. We apply our results to iid compositions of uniformly expanding circle maps, to iid compositions of the Gauss-Rényi maps (random continued fractions) and to iid compositions of Pomeau-Manneville maps.

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