2019/10/04 by Alexandros Margaris, Margaris, Alexandros, Eric J. Olson +3
Computer Science · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories #math.DS
paper · pdf · doi:10.48550/arxiv.1910.01835
30 pages
openalex publication_date 2019/10/04 · arxiv created 2020/01/08 · arxiv updated 2020/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If X is a set with finite Assouad dimension, it is known that the Assouad dimension of X-X does not necessarily obey any non-trivial bound in terms of the Assouad dimension of X. In this paper, we consider self-similar sets on the real line and we show that if a particular weak separation condition is satisfied, then the Assouad dimension of the set of differences is bounded above by twice the Assouad dimension of the set itself. We then apply this result to a particular class of asymmetric Cantor sets.