The OSC does not imply the SOSC for infinite iterated function systems
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- by Tomasz Szarek and Stanisław Wȩdrychowicz PDF
- Proc. Amer. Math. Soc. 133 (2005), 437-440 Request permission
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.References
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Additional Information
- Tomasz Szarek
- Affiliation: Institute of Mathematics, Silesian University – and – Institute of Mathematics of the Polish Academy of Sciences, Bankowa 14, 40–007 Katowice, Poland
- Email: szarek@ux2.math.us.edu.pl
- Stanisław Wȩdrychowicz
- Affiliation: Department of Mathematics, Technical University of Rzeszów, W. Pola 6, 35–959 Rzeszów, Poland
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 133 (2005), 437-440
- MSC (2000): Primary 28A80; Secondary 28A78
- DOI: https://doi.org/10.1090/S0002-9939-04-07708-1
- MathSciNet review: 2093065