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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.
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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