Central Limit Theorem for Sequential Dynamical Systems

Abstract

We present a general approach to establish the Central Limit Theorem with error bounds for sequential dynamical systems. The main tool we develop is the application to this setting of a projective metric on complex cones, following the ideas introduced by Rugh and Dubois. To demonstrate the power of the proposed setting, we apply it to both sequential expanding maps, where similar results are known, and to sequential dispersing billiards, for which no such results are currently known.