Self-Similar Jordan Arcs Which Do Not Satisfy OSC

Abstract

It was proved in 2007 by C.Bandt and H.Rao that if a system $S=\{S_1,...,S_m\}$ of contraction similarities in $R^2$ with a connected attractor $K$ has the finite intersection property, then it satisfies OSC. We construct a self-simiilar Jordan arc in $R^3$, defined by a system $S$ , which does not satisfy OSC and at the same time has one-point intersection property.

23 pages, 6 figures, 2 tables

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