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

Authors: Tomasz Szarek and Stanislaw Wedrychowicz
Journal: Proc. Amer. Math. Soc. 133 (2005), 437-440
MSC (2000): Primary 28A80; Secondary 28A78
Published electronically: September 2, 2004
MathSciNet review: 2093065
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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.

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Tomasz Szarek
Affiliation: Institute of Mathematics, Silesian University – and – Institute of Mathematics of the Polish Academy of Sciences, Bankowa 14, 40–007 Katowice, Poland

Stanislaw Wedrychowicz
Affiliation: Department of Mathematics, Technical University of Rzeszów, W. Pola 6, 35–959 Rzeszów, Poland

Keywords: Fractal, open set condition, strong open set condition
Received by editor(s): July 2, 2003
Published electronically: September 2, 2004
Additional Notes: The first author’s research was supported by the State Committee for Scientific Research Grant No. Z PO3A 031 25
Communicated by: Michael Handel
Article copyright: © Copyright 2004 American Mathematical Society

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