When the weak separation condition implies the generalized finite type condition. (English) Zbl 1466.28010

In this well-written paper, the authors prove that an iterated function system (IFS) of similarities on \(\mathbb R\) that satisfies the weak separation condition and has an interval \([0,1]\) as its self-similar set is of generalized finite type. But it is unknown if the assumption that the self-similar set is an interval is necessary. In addition, the IFS satisfies the convex generalized finite type condition if and only if it satisfies the finite neighbour condition.


28A80 Fractals
Full Text: DOI arXiv


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