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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


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