2021/02/11 by Simon Baker, Baker, Simon
Computer Science · Mathematics · #Advanced Topology and Set Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Metric Geometry (math.MG) #Number Theory (math.NT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2102.05979
openalex publication_date 2021/02/11 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28
In this paper we obtain new lower bounds for the upper box dimension of αβ sets. As a corollary of our main result, we show that if α is not a Liouville number and β is a Liouville number, then the upper box dimension of any αβ set is 1. We also use our dimension bounds to obtain new results on affine embeddings of self-similar sets.