ARITHMETIC PRODUCT OF SELF-SIMILAR SETS WITH TWO BRANCHES

Qin Wang () and Kai Zhang
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Qin Wang: College of Big Data and Software Engineering, Zhejiang Wanli University, Ningbo 315101, P. R. China
Kai Zhang: Junior College, Zhejiang Wanli University, Ningbo 315101, P. R. China

FRACTALS (fractals), 2021, vol. 29, issue 02, 1-5

Abstract: For self-similar set E = λ1E ∪ (λ2E + 1 − λ2) (λ1 + λ2 < 1), we study the arithmetic product of E and obtain that when λ1 ≥ λ2 > 0 then E ⋅ E = [0, 1]if and only if λ1 ≥ (1 − λ2)2. To deal with the arithmetic product of self-similar sets with different ratios, we introduce a technique named comparable rectangle.

Keywords: Self-Similar Set; Arithmetic Product; Comparable Rectangle (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500390

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