On Selfsimilar Jordan Curves on the Plane

@article{Aseev2003OnSJ,
  title={On Selfsimilar Jordan Curves on the Plane},
  author={V. Aseev and A. Tetenov and A. Kravchenko},
  journal={Siberian Mathematical Journal},
  year={2003},
  volume={44},
  pages={379-386}
}
We study the attractors of a finite system of planar contraction similarities Sj (j=1,...,n) satisfying the coupling condition: for a set {x0,...,xn} of points and a binary vector (s1,...,sn), called the signature, the mapping Sj takes the pair {x0,xn} either into the pair {xj-1,xj} (if sj =0) or into the pair {xj, xj-1} (if sj=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… Expand
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