Topological classification of scattered IFS-attractors

Details Topological classification of scattered IFS-attractors Topological classification of scattered IFS-attractors

2012-04-21

arxiv.org/abs/1204.4797v1

Mathematics

Dynamical Systems

Scientific paper

Considering countable spaces as attractors of iterated function systems, we construct an example of a convergent sequence of real numbers which is not an IFS-attractor. Moreover we show that that every countable compact metric space of successor height can be embedded topologically in the real line so that it becomes the attractor of an IFS. Furthermore if a countable compact metric space is homeomorphic to any IFS-attractor, then its height is not a limit ordinal.

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