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

2025/06/02 by Jonny Imbierski, Imbierski, Jonny, Charlene Kalle +1
Computer Science · Mathematics · Physics and Astronomy · #11K55 #37H99 #Cellular Automata and Applications #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2506.01803

openalex publication_date 2025/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

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• Hausdorff dimension of particularly non-normal numbers in dynamical systems fulfilling the specification property