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arXiv · 1908.10957

Absolutely Continuous Invariant measures for non-autonomous dynamical systems

Pawel Gora·Abraham Boyarsky·Christopher Keefe
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Abstract

We consider the non autonomous dynamical system $\{τ_{n}\},$ where $τ_{n}$ is a continuous map $X\rightarrow X,$ and $X$ is a compact metric space. We assume that $\{τ_{n}\}$ converges uniformly to $τ.$ The inheritance of chaotic properties as well as topological entropy by $τ$ from the sequence $\{τ_{n}\}$ 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 $τ$ of a non autonomous sequence of maps $\{τ_n\}$ with acims has an acim.

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Pawel Gora, Abraham Boyarsky, Christopher Keefe. 2019-08-28. Absolutely Continuous Invariant measures for non-autonomous dynamical systems. https://doi.org/10.1016/j.jmaa.2018.09.060.

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