Fractal dimensions of continuous piecewise linear iterated function systems

Peter Raith; Károly Simon; R. Dániel Prokaj

doi:10.1090/proc/16430

Fractal dimensions of continuous piecewise linear iterated function systems

Titel in Übersetzung: Fraktale Dimensionen von stetigen stückweise linearen iterierten Funktionssystemen

Peter Raith
, Károly Simon
, R. Dániel Prokaj

Institut für Mathematik

Veröffentlichungen: Beitrag in Fachzeitschrift › Artikel › Peer Reviewed

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.

Titel in Übersetzung	Fraktale Dimensionen von stetigen stückweise linearen iterierten Funktionssystemen
Originalsprache	Englisch
Seiten (von - bis)	4703–4719
Seitenumfang	17
Fachzeitschrift	Proceedings of the American Mathematical Society
Jahrgang	151
Ausgabenummer	11
DOIs	https://doi.org/10.1090/proc/16430
Publikationsstatus	Veröffentlicht - 1 Nov. 2023

ÖFOS 2012

101027 Dynamische Systeme

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10.1090/proc/16430

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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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KW - Hausdorff dimension

KW - Hausdorff dimension.

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Fractal dimensions of continuous piecewise linear iterated function systems

Abstract

ÖFOS 2012

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