Work

Characterization of the algebraic difference of special affine Cantor sets

Year: 2024

Type: article

Abstract: We investigate some self-similar Cantor sets $C(l,r,p)$, which we call S-Cantor sets, generated by numbers $l,r,p \in \N$, $l+r< p$. We give a full characterization of the set $C(l_1,r_1,p)-C(l_2,r_2,p)$ which can take one of the form: the interval $[-1,1]$, a Cantor set, an L-Cantorval, an R-Cantorval or an M-Cantorval. As corollaries we give examples of Cantor sets and Cantorvals, which can be easily described using some positional numeral systems.

Source: Topological Methods in Nonlinear Analysis

DOI: 10.12775/tmna.2023.057

Author: Piotr Nowakowski

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: Grantová Agentura České Republiky

Award: Banach spaces of continuous and Lipschitz functions

OpenAlex ID: W4402822395

FWCI: 0.674

Cites:

Cited by: 1

Related to: 10