Thresholds for one-parameter families of affine iterated function systems*This work was partially supported by a grant from the Simons Foundation (322515 to Andrew Vince). (20th October 2020)

• Record Type: Journal Article
• Authors: Vince, Andrew
• Is Part Of: Nonlinearity. Volume 33:Number 12(2020)
• Page Start: 6541
• Page End: 6563
• Publication Date: 2020-10-20
• Subjects: iterated function system -- attractor -- fractal; 28A80; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/aba237
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: This paper examines thresholds for certain properties of the attractor of a general one-parameter affine family of iterated functions systems. As the parameter increases, the iterated function system becomes less contractive, and the attractor evolves. Thresholds are studied for the following properties: the existence of an attractor, the connectivity of the attractor, and the existence of non-empty interior of the attractor. Also discussed are transition phenomena between existence and non-existence of an attractor.