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

Zugriff auf Dokument

10.1090/proc/16430

Andere Dateien und Links

Verknüpfung zur Publikation in Scopus

Zitationsweisen

@article{5487dc7cfb404538ba22d219708fcce0,

title = "Fractal dimensions of continuous piecewise linear iterated function systems",

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.",

keywords = "Piecewise linear iterated function system, Hausdorff dimension, Hausdorff dimension.",

author = "Peter Raith and K{\'a}roly Simon and Prokaj, {R. D{\'a}niel}",

year = "2023",

month = nov,

day = "1",

doi = "10.1090/proc/16430",

language = "English",

volume = "151",

pages = "4703–4719",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

number = "11",

}

TY - JOUR

T1 - Fractal dimensions of continuous piecewise linear iterated function systems

AU - Raith, Peter

AU - Simon, Károly

AU - Prokaj, R. Dániel

PY - 2023/11/1

Y1 - 2023/11/1

N2 - 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.

AB - 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.

KW - Piecewise linear iterated function system

KW - Hausdorff dimension

KW - Hausdorff dimension.

UR - http://www.scopus.com/inward/record.url?scp=85171421594&partnerID=8YFLogxK

U2 - 10.1090/proc/16430

DO - 10.1090/proc/16430

M3 - Article

VL - 151

SP - 4703

EP - 4719

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 11

ER -

Fractal dimensions of continuous piecewise linear iterated function systems

Abstract

ÖFOS 2012

Zugriff auf Dokument

Andere Dateien und Links

Fingerprint

Zitationsweisen