On nonlinear iterated function systems with overlaps

Boris Solomyak

doi:https://doi.org/10.4171/JFG/150

On nonlinear iterated function systems with overlaps

Boris Solomyak

Department of Mathematics

Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that there is no “dimension drop”.

Original language	English
Pages (from-to)	373-387
Number of pages	15
Journal	Journal of Fractal Geometry
Volume	11
Issue number	3-4
DOIs	https://doi.org/10.4171/JFG/150
State	Published - 2024

Keywords

dimension drop
non-linear iterated function system
overlap

All Science Journal Classification (ASJC) codes

Geometry and Topology
Applied Mathematics

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https://doi.org/10.4171/JFG/150

Cite this

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title = "On nonlinear iterated function systems with overlaps",

abstract = "We construct an example of an iterated function system on the line, consisting of linear fractional transformations, such that two of the maps share a fixed points, but the dimension of the attractor equals the conformal dimension, so that there is no “dimension drop”.",

keywords = "dimension drop, non-linear iterated function system, overlap",

author = "Boris Solomyak",

note = "Publisher Copyright: {\textcopyright}2024 European Mathematical Society.",

year = "2024",

doi = "https://doi.org/10.4171/JFG/150",

language = "الإنجليزيّة",

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KW - dimension drop

KW - non-linear iterated function system

KW - overlap

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DO - https://doi.org/10.4171/JFG/150

M3 - مقالة

SN - 2308-1309

VL - 11

SP - 373

EP - 387

JO - Journal of Fractal Geometry

JF - Journal of Fractal Geometry

IS - 3-4

ER -

On nonlinear iterated function systems with overlaps

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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