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

DOI10.1090/S0002-9939-04-07708-1zbMath1051.28005OpenAlexW1496635796MaRDI QIDQ4825633

Tomasz Szarek, Stanislaw Wedrychowicz

Publication date: 28 October 2004

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-04-07708-1

zbMATH Keywords

fractalsIFSopen set conditionstrong open set conditioncontracting similitudes

Mathematics Subject Classification ID

Fractals (28A80) Hausdorff and packing measures (28A78)

Related Items (10)

Graph directed Markov systems on Hilbert spaces ⋮ Spectral asymptotics of one-dimensional fractal Laplacians in the absence of second-order identities ⋮ SEPARATION PROPERTIES FOR BI-LIPSCHITZ ITERATED FUNCTION SYSTEMS ⋮ Ruelle operator for infinite conformal iterated function systems ⋮ Quantization coefficients in infinite systems ⋮ Infinite graph-directed systems and Hausdorff dimension ⋮ Separation properties for infinite iterated function systems ⋮ Analytic multifunctions, holomorphic motions and Hausdorff dimension in iFSs ⋮ Infinite iterated function systems with overlaps ⋮ On hyperbolic affine generalized infinite iterated function systems

Cites Work

• Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets
• On the structure of self-similar sets
• Separation Properties for Self-Similar Sets
• Dimensions and Measures in Infinite Iterated Function Systems
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