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arXiv · 1512.00290

Self-Similar Jordan Arcs Which Do Not Satisfy OSC

Andrey Tetenov·Kirill Kamalutdinov·Dmitry Vaulin
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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.

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Andrey Tetenov, Kirill Kamalutdinov, Dmitry Vaulin. 2016-01-15. Self-Similar Jordan Arcs Which Do Not Satisfy OSC. https://arxiv.org/abs/1512.00290

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