Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Fractal Geometry and Stochastics IVTransformations Between Fractals

Fractal Geometry and Stochastics IV: Transformations Between Fractals [We observe that there exists a natural homeomorphism between the attractors of any two iterated function systems, with coding maps, that have equivalent address structures. Then we show that a generalized Minkowski metric may be used to establish conditions under which an affine iterated function system is hyperbolic. We use these results to construct families of fractal homeomorphisms on a triangular subset of ℝ2. We also give conditions under which certain bilinear iterated function systems are hyperbolic and use them to generate families of homeomorphisms on the unit square. These families are associated with “tilings” of the unit square by fractal curves, some of whose box-counting dimensions can be given explicitly.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Fractal Geometry and Stochastics IVTransformations Between Fractals

Part of the Progress in Probability Book Series (volume 61)
Editors: Bandt, Christoph; Zähle, Martina; Mörters, Peter
Barnsley, Michael F.
Fractal Geometry and Stochastics IV — Dec 30, 2009
Download PDF
23 pages

Loading next page...
 
/lp/springer-journals/fractal-geometry-and-stochastics-iv-transformations-between-fractals-cIymDEYeN7

References (18)

Publisher
Birkhäuser Basel
Copyright
© Birkhäuser Basel 2009
ISBN
978-3-0346-0029-3
Pages
227 –250
DOI
10.1007/978-3-0346-0030-9_8
Publisher site
See Chapter on Publisher Site

Abstract

[We observe that there exists a natural homeomorphism between the attractors of any two iterated function systems, with coding maps, that have equivalent address structures. Then we show that a generalized Minkowski metric may be used to establish conditions under which an affine iterated function system is hyperbolic. We use these results to construct families of fractal homeomorphisms on a triangular subset of ℝ2. We also give conditions under which certain bilinear iterated function systems are hyperbolic and use them to generate families of homeomorphisms on the unit square. These families are associated with “tilings” of the unit square by fractal curves, some of whose box-counting dimensions can be given explicitly.]

Published: Dec 30, 2009

Keywords: 37E30; 28A80; 37B10; Iterated function systems; symbolic dynamics; dynamical systems

There are no references for this article.