Measure preserving fractal homeomorphisms
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Altmetric Citations
Barnsley, Michael; Harding, Brendan; Rypka, Miroslav
Description
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]
dc.contributor.author | Barnsley, Michael | |
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dc.contributor.author | Harding, Brendan | |
dc.contributor.author | Rypka, Miroslav | |
dc.coverage.spatial | Kochi India | |
dc.date.accessioned | 2015-12-10T22:26:02Z | |
dc.date.created | November 13-16 2013 | |
dc.identifier.isbn | 9783319081045 | |
dc.identifier.uri | http://hdl.handle.net/1885/53743 | |
dc.description.abstract | 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 examples are illustrated and applications to computer aided design and manufacture, via three-dimensional printing, are envisaged. | |
dc.publisher | Springer | |
dc.relation.ispartofseries | 1st International Conference and Workshop on Fractals and Wavelets, ICFW India | |
dc.source | Springer Proceedings in Mathematics and Statistics | |
dc.source.uri | http://dx.doi.org/10.1007/978-3-319-08105-2 | |
dc.title | Measure preserving fractal homeomorphisms | |
dc.type | Conference paper | |
local.description.notes | Imported from ARIES | |
local.description.refereed | Yes | |
dc.date.issued | 2014 | |
local.identifier.absfor | 010100 - PURE MATHEMATICS | |
local.identifier.absfor | 010204 - Dynamical Systems in Applications | |
local.identifier.ariespublication | a383154xPUB282 | |
local.type.status | Published Version | |
local.contributor.affiliation | Barnsley, Michael, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Harding, Brendan, College of Physical and Mathematical Sciences, ANU | |
local.contributor.affiliation | Rypka, Miroslav, College of Physical and Mathematical Sciences, ANU | |
local.description.embargo | 2037-12-31 | |
local.bibliographicCitation.startpage | 79 | |
local.bibliographicCitation.lastpage | 102 | |
local.identifier.doi | 10.1007/978-3-319-08105-2_5 | |
local.identifier.absseo | 970101 - Expanding Knowledge in the Mathematical Sciences | |
dc.date.updated | 2015-12-09T09:29:20Z | |
local.identifier.scopusID | 2-s2.0-84910621564 | |
Collections | ANU Research Publications |
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