Dimension Of Inhomogeneous Sub-Self-Similar Sets
Dynamical Systems
2026-01-29 v2
Abstract
In this paper, we introduce the concept of Inhomogeneous sub-self-similar (ISSS) sets, building upon the foundations laid by Falconer (Trans. Amer. Math. Soc. 347 (1995) 3121-3129) in the study of sub-self-similar sets and drawing inspiration from Barnsley's work on inhomogeneous self-similar sets (Proc. Roy. Soc. London Ser. A 399 (1985), no. 1817, 24). We explore a range of examples of ISSS sets and elucidate a method to construct ISSS sets. We also investigate the upper and lower box dimensions of ISSS sets and discuss the continuity of the Hausdorff dimension.
Keywords
Cite
@article{arxiv.2508.18706,
title = {Dimension Of Inhomogeneous Sub-Self-Similar Sets},
author = {Shivam Dubey and Saurabh Verma},
journal= {arXiv preprint arXiv:2508.18706},
year = {2026}
}