Dimension of Besicovitch-Eggleston sets for non-autonomous systems with countable symbolic dynamics

Abstract

In this article we derive a formula for the Hausdorff dimension of Besicovitch-Eggleston level sets associated with non-autonomous dynamics constructed from families of countable affine iterated function systems. The formula obtained shows that the universal-lower-bound phenomenon present in the autonomous case studied by Fan et al. (2010) persists in this non-autonomous setting.

23 pages, 2 figures