The OSC does not imply the SOSC for infinite iterated function systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The OSC does not imply the SOSC for infinite iterated function systems

Authors:	Tomasz Szarek Stanislaw Wedrychowicz

Institution:	Institute of Mathematics, Silesian University -- and -- Institute of Mathematics of the Polish Academy of Sciences, Bankowa 14, 40--007 Katowice, Poland ; Department of Mathematics, Technical University of Rzeszów, W. Pola 6, 35--959 Rzeszów, Poland

Abstract:	It is shown that every class of contracting similitudes $\{f_{1},\ldots , f_{N}\}$ on $R^{s}$ satisfying the OSC and such that $\dim _{H} \mathcal{K}_{0}<s$ , where $\mathcal{K}_{0}$ denotes the corresponding fractal, can be extended to an infinite family of contracting similitudes which still satisfies the OSC but the SOSC does not hold.

Keywords:	Fractal open set condition strong open set condition

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