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2020 Generalized Cantor functions: random function iteration
Jordan Armstrong, Lisbeth Schaubroeck
Involve 13(2): 281-299 (2020). DOI: 10.2140/involve.2020.13.281

Abstract

We provide a generalization of the classical Cantor function. One characterization of the Cantor function is generated by a sequence of real numbers that starts with a seed value and at each step randomly applies one of two different linear functions. The Cantor function is defined as the probability that this sequence approaches infinity. We generalize the Cantor function to instead use a set of any number of linear functions with integer coefficients. We completely describe the resulting probability function and give a full explanation of which intervals of seed values lead to a constant probability function value.

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Jordan Armstrong. Lisbeth Schaubroeck. "Generalized Cantor functions: random function iteration." Involve 13 (2) 281 - 299, 2020. https://doi.org/10.2140/involve.2020.13.281

Information

Received: 13 May 2019; Revised: 11 December 2019; Accepted: 23 December 2019; Published: 2020
First available in Project Euclid: 25 June 2020

zbMATH: 07184485
MathSciNet: MR4080495
Digital Object Identifier: 10.2140/involve.2020.13.281

Subjects:
Primary: 26A18

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.13 • No. 2 • 2020
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