On cut sets of attractors of iterated function systems

Loridant, Benoît; Luo, Jun; Sellami, Tarek; Thuswaldner, Jörg

doi:10.1090/proc/13182

On cut sets of attractors of iterated function systems
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by Benoît Loridant, Jun Luo, Tarek Sellami and Jörg M. Thuswaldner PDF

Proc. Amer. Math. Soc. 144 (2016), 4341-4356 Request permission

Abstract:

In this paper, we study cut sets of attractors of iterated function systems (IFS) in $\mathbb {R}^d$. Under natural conditions, we show that all irreducible cut sets of these attractors are perfect sets or single points. This leads to a criterion for the existence of cut points of IFS attractors. If the IFS attractors are self-affine tiles, our results become algorithmically checkable and can be used to exhibit cut points with the help of Hata graphs. This enables us to construct cut points of some self-affine tiles studied in the literature.

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