Tetenov, A. V. On the rigidity of one-dimensional systems of contraction similitudes. (English) Zbl 1119.28007 Sib. Èlektron. Mat. Izv. 3, 342-345 (2006). The main result reads as follows: Let \(S=\{S_1,\dots, S_m\}\), \(T=\{T_1,\dots, T_m\}\) be systems of contraction similitudes in \(\mathbb R\), the invariant set of each being the segment \([0, 1]\), and let \(\varphi: K(S)\to K(T)\) be a structure-preserving homeomorphism for these two systems, such that \(\varphi(0)=0\) and \(\varphi(1)=1\). If \(Id\) is a limit point of the associated family \(F(S)\) for the system \(S\), then \(\varphi(x)\equiv x\), and \(S=T\). Reviewer: Victor Alexandrov (Novosibirsk) Cited in 4 Documents MSC: 28A80 Fractals 52C25 Rigidity and flexibility of structures (aspects of discrete geometry) Keywords:expansion ratio; contraction map; structure-preserving homeomorphism PDFBibTeX XMLCite \textit{A. V. Tetenov}, Sib. Èlektron. Mat. Izv. 3, 342--345 (2006; Zbl 1119.28007) Full Text: EuDML