Geodesic
Generating iterated function systems for self-similar sets with a separation condition
Yuanyuan Yao1
1 Department of Mathematics East China University of Science and Technology Shanghai 200237, P.R. China
Fundamenta Mathematicae, Tome 237 (2017) no. 2, pp. 127-133 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Let $\{f_i\}_{i=1}^m$ be an iterated function system (IFS) for a self-similar set $E\subseteq {\mathbb R}^d$ (which is not a singleton) with the smallest integer $m\ge 2$. Suppose the distance of any two sets of the form $f_{i_1}(E)$ and $f_{i_2}(E)$ is strictly larger than the diameter of any $f_i(E)$. Then the semigroup of all generating IFSs for $E$, equipped with the composition as product, is finitely generated. This partially answers a question posed by Elekes, Keleti and Máthé.
DOI : 10.4064/fm88-10-2016
Keywords: iterated function system ifs self similar set subseteq mathbb which singleton smallest integer suppose distance sets form strictly larger diameter semigroup generating ifss equipped composition product finitely generated partially answers question posed elekes keleti

Yuanyuan Yao 1

1 Department of Mathematics East China University of Science and Technology Shanghai 200237, P.R. China 
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Yuanyuan Yao. Generating iterated function systems for self-similar sets with a separation condition. Fundamenta Mathematicae, Tome 237 (2017) no. 2, pp. 127-133. doi: 10.4064/fm88-10-2016

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