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

TL;DR

This paper derives a formula for the Hausdorff dimension of Besicovitch-Eggleston level sets in non-autonomous systems with countable symbolic dynamics, extending known phenomena from autonomous cases.

Contribution

It provides a new dimension formula for non-autonomous affine iterated function systems, demonstrating the persistence of the universal-lower-bound phenomenon.

Findings

The Hausdorff dimension formula applies to non-autonomous systems with countable symbolic dynamics.

The universal-lower-bound phenomenon persists in the non-autonomous setting.

The results extend previous autonomous case studies to more general non-autonomous systems.

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.