Shinohara, Katsutoshi Some examples of minimal Cantor sets for iterated function systems with overlap. (English) Zbl 1351.37166 Tokyo J. Math. 37, No. 1, 225-236 (2014). 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. Cited in 2 Documents 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 Keywords:Cantor set; semigroup action; minimality PDFBibTeX XMLCite \textit{K. Shinohara}, Tokyo J. Math. 37, No. 1, 225--236 (2014; Zbl 1351.37166) Full Text: DOI arXiv Euclid 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 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.