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Hare, Kathryn E.; Hare, Kevin G.; Rutar, Alex

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

Proc. Am. Math. Soc. 149, No. 4, 1555-1568 (2021).
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.
Reviewer: Wen-hui Ai (Changsha)

Cited in 4 Documents

MSC:

28A80 Fractals

Keywords:

self-similar set; weak separation condition; finite type; generalized finite type
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Full Text: DOI arXiv

References:

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