4 research outputs found
Absolutely Continuous Invariant measures for non-autonomous dynamical systems
We consider the non autonomous dynamical system where
is a continuous map and is a compact metric
space. We assume that converges uniformly to The
inheritance of chaotic properties as well as topological entropy by
from the sequence 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 of a non autonomous sequence of maps
with acims has an acim