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Some examples of minimal Cantor sets for iterated function systems with overlap. (English) Zbl 1351.37166

Summary: We give some examples of iterated function systems (IFSs) with overlap on the interval such that the semigroup action they give rise to has a minimal set homeomorphic to the Cantor set.

MSC:

37E05 Dynamical systems involving maps of the interval
37B05 Dynamical systems involving transformations and group actions with special properties (minimality, distality, proximality, expansivity, etc.)
28A80 Fractals
39B12 Iteration theory, iterative and composite equations
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References:

[1] P. Barrientos and A. Raibekas, Dynamics of iterated function systems on the circle close to rotations, preprint, available fromhttp://arxiv.org/abs/1303.2521 · Zbl 1352.37121
[2] K. Shinohara, On the minimality of semigroup actions on the interval which are \(C^1\)-close to the identity, preprint, available from http://arxiv.org/abs/1210.0112
[3] A. Navas, Groups of circle diffeomorphisms , Translation of the 2007 Spanish edition. Chicago Lectures in Mathematics. University of Chicago Press, Chicago, IL, 2011. xviii+290 pp. · Zbl 1163.37002
[4] H. Sumi, Interaction cohomology of forward or backward self-similar systems, Adv. Math. 222 (2009), no. 3, 729-781. · Zbl 1180.37054 · doi:10.1016/j.aim.2009.04.007
[5] S. Willard, General topology , Dover Publications, Inc., Mineola, NY, 2004. xii+369 pp. · Zbl 1052.54001
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