2021/02/11 by Simon Baker, Baker, Simon
Computer Science · Mathematics · #Advanced Topology and Set Theory #Affine transformation #Alpha (finance) #BETA (programming language) #Combinatorics #Computer science #Corollary #Dimension (graph theory) #Discrete mathematics #Dynamical Systems (math.DS) #Effective dimension #FOS: Mathematics #Fractal dimension #Hausdorff dimension #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Metric Geometry (math.MG) #Minkowski–Bouligand dimension #Number Theory (math.NT) #Packing dimension #Pure mathematics #Set (abstract data type) #Statistics #Upper and lower bounds #math.DS #math.MG #math.NT #semigroups and automata theory
paper · pdf · open access · doi:10.48550/arxiv.2102.05979
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/02/11 · openalex publication_date 2021/02/11 · arxiv updated 2021/02/12 · 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.