https://doi.org/10.1140/epjs/s11734-025-01578-z
Regular Article
Dimensional analysis of graphs of fractal functions as invariant sets for some dynamical systems associated with composite mappings
School of Mathematics and Statistics, Nanjing University of Science and Technology, 210094, Nanjing, China
Received:
23
July
2024
Accepted:
14
March
2025
Published online:
6
May
2025
This article explores the fractal dimension of graphs of fractal functions as invariant sets for some dynamical systems associated with composite mappings. We mainly focus on the issue that how the fractal dimension of graphs of continuous functions varies under compound operations, which has been separately discussed from two aspects: the variation of the outer function and the variation of the inner function. The corresponding dimensional results have been derived when the outer and the inner function, respectively, are taken as a Lipschitz or bi-Lipschitz function. On this basis, concrete applications in dynamical systems have been provided when graphs of fractal functions are interpreted as fractal basin boundaries for them. Furthermore, numerical simulations of some specific examples have also been performed to corroborate our theoretical results. This work may contribute to the dimensional theory of graphs of fractal functions and have certain practical application significance in the dynamical systems theory and other natural sciences.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
