Abstract
We study the attractors of a finite system of planar contraction similarities S j (j=1,...,n) satisfying the coupling condition: for a set {x 0,...,x n} of points and a binary vector (s 1,...,s n ), called the signature, the mapping S j takes the pair {x 0,x n} either into the pair {x j-1,x j } (if s j =0) or into the pair {x j , x j-1} (if s j =1). We describe the situations in which the Jordan property of such attractor implies that the attractor has bounded turning, i.e., is a quasiconformal image of an interval of the real axis.
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Aseev, V.V., Tetenov, A.V. & Kravchenko, A.S. On Selfsimilar Jordan Curves on the Plane. Siberian Mathematical Journal 44, 379–386 (2003). https://doi.org/10.1023/A:1023848327898
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DOI: https://doi.org/10.1023/A:1023848327898