Dimensions associated with recurrent self-similar sets

DOI10.1017/S0305004100070407zbMath0742.28002OpenAlexW2123131866MaRDI QIDQ3982361

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Publication date: 26 June 1992

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

Full work available at URL: https://doi.org/10.1017/s0305004100070407

zbMATH Keywords

Hausdorff dimensionbox dimensionergodic dynamical systemergodic invariant measurerecurrent iterated function systemexact-dimensionality of measurerecurrent self- similar set

Mathematics Subject Classification ID

Fractals (28A80) Ergodic theory (37A99) Hausdorff and packing measures (28A78)

Related Items (13)

Dimension bounds for invariant measures of bi-Lipschitz iterated function systems ⋮ Hausdorff dimensions of sofic affine-invariant sets ⋮ Unimodular Pisot substitutions and their associated tiles ⋮ Box dimensions of (\timesm,\timesn)-invariant sets ⋮ On dimension of fractal functions on product of the Sierpiński gaskets and associated measures ⋮ A Compact Framework for Hidden Markov Chains with Applications to Fractal Geometry ⋮ Asymptotic of the geometric mean error in the quantization of recurrent self-similar measures ⋮ Singularity of self-similar measures with respect to Hausdorff measures ⋮ The pointwise dimension of self-similar measures in complete metric spaces ⋮ Convergence order of the geometric mean errors for Markov-type measures ⋮ Local dimensions and quantization dimensions in dynamical systems ⋮ Dimension of homogeneous rational self-similar measures with overlaps ⋮ TheL^q-spectrum of a class of graph directed self-affine measures

Cites Work

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• The calculus of fractal interpolation functions
• Recurrent iterated function systems
• An exact formula for the measure dimensions associated with a class of piecewise linear maps
• The Hausdorff dimension of general Sierpiński carpets
• Hidden Variable Fractal Interpolation Functions
• Dimension and Dynamics for Fractal Recurrent Sets
• Dimensions and Measures of Quasi Self-Similar Sets

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