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Abstract
We consider iterated function systems on the unit interval generated by two contractive similarity transformations with the same similarity ratio. When the ratio is greater than or equal to $1/2$, the limit set is the interval itself and the code map is not one-to-one. We study the set of points of the limit set having unique addresses. We obtain a formula for the Hausdorff dimension of the set when the similarity ratio belongs to certain intervals by applying the concept of graph directed Markov system.
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