Skip navigation
Skip navigation

Measure preserving fractal homeomorphisms

Barnsley, Michael; Harding, Brendan; Rypka, Miroslav


The basic theory of fractal transformations is recalled. For a fractal homeomorphism generated by a pair of affine iterated function systems (IFSs), a condition under which the transformation is measure (i.e. area, volume, etc.) preserving is established. Then three families of fractal homeomorphisms, two of them entirely new, generated by pairs of affine IFSs, are introduced. It is proved that they admit subfamilies that preserve n-dimensional Lebesque measure, where n is 2 or 3. Several...[Show more]

CollectionsANU Research Publications
Date published: 2014
Type: Conference paper
Source: Springer Proceedings in Mathematics and Statistics
DOI: 10.1007/978-3-319-08105-2_5


File Description SizeFormat Image
01_Barnsley_Measure_preserving_fractal_2014.pdf434.26 kBAdobe PDF    Request a copy

Items in Open Research are protected by copyright, with all rights reserved, unless otherwise indicated.

Updated:  20 July 2017/ Responsible Officer:  University Librarian/ Page Contact:  Library Systems & Web Coordinator