Dimension of slices through the Sierpinski carpet

DOI10.1090/S0002-9947-2012-05586-3zbMath1273.28005MaRDI QIDQ4915335

Anthony Manning, Károly Simon

Publication date: 10 April 2013

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

zbMATH Keywords

projectionHausdorff dimensionbox counting dimensionself-similar setsdimension of fibers

Mathematics Subject Classification ID

Ergodic theorems, spectral theory, Markov operators (37A30) Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents (37H15) Fractals (28A80) Symbolic dynamics (37B10) Hausdorff and packing measures (28A78) Dimension theory of smooth dynamical systems (37C45)

Related Items (16)

Slices of Hewitt-Stromberg measures and co-dimensions formula ⋮ Exact dimensionality and projections of random self-similar measures and sets ⋮ Fractal percolations ⋮ The topological Hausdorff dimension and transport properties of Sierpiński carpets ⋮ Incidence problems in harmonic analysis, geometric measure theory, and ergodic theory. Abstracts from the workshop held June 4--9, 2023 ⋮ Self-Similar Sets: Projections, Sections and Percolation ⋮ Hausdorff dimension of the level sets of self-affine functions ⋮ Singularity versus exact overlaps for self-similar measures ⋮ Dimension of slices of Sierpiński-like carpets ⋮ On the dilatational wave motion in anisotropic fractal solids ⋮ Spatially independent martingales, intersections, and applications ⋮ Dimension of slices through fractals with initial cubic pattern ⋮ Differentiable points of Sierpinski-like sponges ⋮ Multifractal geometry of slices of measures ⋮ Arithmetic representations of real numbers in terms of self-similar sets ⋮ Sets which are not tube null and intersection properties of random measures

Cites Work

• Growth rate for beta-expansions
• Non-negative matrices and Markov chains. 2nd ed
• Intersecting random translates of invariant Cantor sets
• Domains of analytic continuation for the top Lyapunov exponent
• Dimension theory of iterated function systems
• Dimension, entropy and Lyapunov exponents
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation
• Noncommuting Random Products
• DIMENSIONS OF INTERSECTIONS OF THE SIERPINSKI CARPET WITH LINES OF RATIONAL SLOPES
• Some Fundamental Geometrical Properties of Plane Sets of Fractional Dimensions
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