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Attractors of iterated function systems with uncountably many maps and infinite sums of Cantor sets.
- Source :
-
Journal of Fractal Geometry . 2017, Vol. 4 Issue 3, p215-256. 42p. - Publication Year :
- 2017
-
Abstract
- We study the topological properties of attractors of iterated function systems (IFS) on the real line, consisting of affine maps of homogeneous contraction ratio. These maps define what we call a second generation IFS: they are uncountably many and the set of their fixed points is a Cantor set. We prove that when this latter either is the attractor of a finite, non-singular, hyperbolic, IFS (of first generation), or it possesses a particular dissection property, the attractor of the second generation IFS is the union of a finite number of closed intervals. We also prove a theorem that generalizes this result to certain infinite sums of compact sets, in the sense of Minkowski and under the Hausdorff metric. [ABSTRACT FROM AUTHOR]
- Subjects :
- *CANTOR sets
*MINKOWSKI geometry
*HAUSDORFF measures
Subjects
Details
- Language :
- English
- ISSN :
- 23081309
- Volume :
- 4
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Journal of Fractal Geometry
- Publication Type :
- Academic Journal
- Accession number :
- 134241339
- Full Text :
- https://doi.org/10.4171/JFG/50