Fractal analysis of Guthrie-Nymann's set and its generalisations
Dynamical Systems
2024-08-27 v2
Abstract
In this paper, we study the fractal properties of the boundary of the Cantorval connected with Guthrie-Nymann's series. In particular, we prove that such a Cantorval can be represented as a union of open intervals and a Cantor set having zero Lebesgue measure and a fractional Hausdorff dimension. Moreover, we extend the result to a countable family of Cantorvals with a similar structure.
Cite
@article{arxiv.2405.16576,
title = {Fractal analysis of Guthrie-Nymann's set and its generalisations},
author = {Mykola Pratsiovytyi and Dmytro Karvatskyi},
journal= {arXiv preprint arXiv:2405.16576},
year = {2024}
}