Fractal dimensions of continuous piecewise linear iterated function systems
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...
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| Veröffentlicht in: | Proceedings of the American Mathematical Society 2023-11, Vol.151 (11), p.4703-4719 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | 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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| ISSN: | 0002-9939 1088-6826 |
| DOI: | 10.1090/proc/16430 |