Classifying functions via growth rates of repeated iterations

We develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations, for example, $n+2\to 2n\to 2^n\to 2^{\cdot ^{\cdot ^2}}$

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Publication Details

Journal
Fundamenta Mathematicae
Published
2024-11-28
DOI
https://doi.org/10.4064/fm316-8-2024
Primary Topic
Iterative Methods for Nonlinear Equations
Type
article
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article

Classifying functions via growth rates of repeated iterations

Titus Hilberdink
Fundamenta Mathematicae
Iterative Methods for Nonlinear Equations
article

Classifying functions via growth rates of repeated iterations

Titus Hilberdink
article en

Abstract

We develop a classification of real functions based on growth rates of repeated iteration. We show how functions are naturally distinguishable when considering inverses of repeated iterations, for example, $n+2\to 2n\to 2^n\to 2^{\cdot ^{\cdot ^2}}$

Fundamenta MathematicaeVol. 268(1)
Nanjing University of Information Science and Technology (CN), Nanjing University of Science and Technology (CN)
Openalex Percentile: Top 67%
Iterative Methods for Nonlinear Equations
DOISourceOpenAlex
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Classifying functions via growth rates of repeated iterations — Titus Hilberdink · Fundamenta Mathematicae (2024) | TGRS Research Map | TGRS