Fractal dimensions of continuous piecewise linear iterated function systems

Prokaj, R.; Raith, Peter; Simon, Károly

doi:10.1090/proc/16430

Fractal dimensions of continuous piecewise linear iterated function systems
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by R. Dániel Prokaj, Peter Raith and Károly Simon;

Proc. Amer. Math. Soc. 151 (2023), 4703-4719

DOI: https://doi.org/10.1090/proc/16430

Published electronically: July 28, 2023

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Abstract:

We consider iterated function systems on the real line that consist of continuous, piecewise linear functions. Under a mild separation condition, we show that the Hausdorff and box dimensions of the attractor are equal to the minimum of 1 and the exponent which comes from the most natural system of covers of the attractor.

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