Graphs induced by iterated function systems |
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Authors: | Xiang-Yang Wang |
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Institution: | 1. School of Mathematics and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, P. R. China
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Abstract: | For an iterated function system (IFS) of similitudes, we define two graphs on the representing symbolic space. We show that if the self-similar set \(K\) has positive Lebesgue measure or the IFS satisfies the weak separation condition, then the graphs are hyperbolic; moreover the hyperbolic boundaries are homeomorphic to the self-similar sets. |
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