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arXiv · 2202.11502

Graphs of continuous functions and fractal dimension

Manuj Verma·Amit Priyadarshi
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Abstract

In this paper, we show that, for any $\beta \in [1,2]$, a given strictly positive real-valued continuous function on $[0,1]$ whose graph has upper box-counting dimension less than or equal to $\beta $ can be decomposed as a product of two real-valued continuous functions on $[0,1]$ whose graphs have upper box-counting dimension equal to $\beta$. We also obtain a formula for the upper box-counting dimension of every element of a ring of polynomials in finite number of continuous functions on $[0,1]$ over the field $\mathbb{R}.$

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Manuj Verma, Amit Priyadarshi. 2022-02-23. Graphs of continuous functions and fractal dimension. https://doi.org/10.1016/j.chaos.2023.113513

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