We consider the non autonomous dynamical system $\{ \tau_{ n}\},$ where $\tau_{ n}$ is a continuous map $X\rightarrow X,$ and $X$ is a compact metric space. We assume that $\{ \tau_{ n}\}$ converges uniformly to $\tau .$ The inheritance of chaotic properties as well as topological entropy by $\tau $ from the sequence $\{ \tau_{ n}\}$ has been studied in \cite{ Can1, Can2, Li,Ste,Zhu}. In \cite{ You} the generalization of SRB\ measures to non-autonomous systems has been considered. In this paper we study absolutely continuous invariant measures (acim) for non autonomous systems. After generalizing the Krylov-Bogoliubov Theorem \cite{ KB} and Straube's Theorem \cite{ Str} to the non autonomous setting, we prove that under certain conditions the limit map $\tau $ of a non autonomous sequence of maps $\{ \tau_n\}$ with acims has an acim.
Categories: math.DS