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Inhomogeneous attractors and box dimension

Name: Inhomogeneous attractors and box dimension
Creator: Fraser, Jonathan M.
Keywords: Mathematics - Metric Geometry, 28A80, 26A18, 37F32, FOS: Mathematics, Metric Geometry (math.MG), Dynamical Systems (math.DS), Mathematics - Dynamical Systems

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2024Embargo end date: 01 Jan 2024Publisher:arXiv

Authors: Fraser, Jonathan M.;

doi: 10.48550/arxiv.2407.08404

arXiv: http://arxiv.org/abs/2407.08404

Inhomogeneous attractors and box dimension

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Abstract

Iterated function systems (IFSs) are one of the most important tools for building examples of fractal sets exhibiting some kind of `approximate self-similarity'. Examples include self-similar sets, self-affine sets etc. A beautiful variant on the standard IFS model was introduced by Barnsley and Demko in 1985 where one builds an \emph{inhomogeneous} attractor by taking the closure of the orbit of a fixed compact condensation set under a given standard IFS. In this expository article I will discuss the dimension theory of inhomogeneous attractors, giving several examples and some open questions. I will focus on the upper box dimension with emphasis on how to derive good estimates, and when these estimates fail to be sharp.

Expository article. 18 pages, 6 figures

Keywords

Mathematics - Metric Geometry, 28A80, 26A18, 37F32, FOS: Mathematics, Metric Geometry (math.MG), Dynamical Systems (math.DS), Mathematics - Dynamical Systems

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