Dimensions of some fractals defined via the semigroup generated by 2 and 3

DOI10.1007/s11856-013-0058-zzbMath1295.28012arXiv1206.4742OpenAlexW2086699131MaRDI QIDQ2017137

Stéphane Seuret, Joerg Schmeling, Yuval Peres, B. M. Solomyak

Publication date: 25 June 2014

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.4742

zbMATH Keywords

Hausdorff dimensionMinkowski dimensionsemigroup action

Mathematics Subject Classification ID

Semigroups of transformations, relations, partitions, etc. (20M20) Fractals (28A80) Symbolic dynamics (37B10) Hausdorff and packing measures (28A78)

Related Items (13)

Multifractal analysis of some multiple ergodic averages ⋮ Dimensions of ‘self-affine sponges’ invariant under the action of multiplicative integers ⋮ Topologically mixing properties of multiplicative integer systems ⋮ On the entropy of multidimensional multiplicative integer subshifts ⋮ Path sets in one-sided symbolic dynamics ⋮ Boundary complexity and surface entropy of 2-multiplicative integer systems on Nd ⋮ The entropy of multiplicative subshifts on trees ⋮ Large deviation principle of nonconventional ergodic averages ⋮ Multifractal analysis of weighted ergodic averages ⋮ Multifractal analysis of some multiple ergodic averages in linear Cookie-Cutter dynamical systems ⋮ On \(\sim\) bisimple right type B \(\omega\)-semigroups as model of some fractal structure ⋮ Large deviation principle of multidimensional multiple averages on \(\mathbb{N}^d\) ⋮ Pattern generation problems arising in multiplicative integer systems

Cites Work

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• Multifractal analysis of multiple ergodic averages
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• A NONCONVENTIONAL STRONG LAW OF LARGE NUMBERS AND FRACTAL DIMENSIONS OF SOME MULTIPLE RECURRENCE SETS
• Double recurrence and almost sure convergence.
• Hausdorff dimension for fractals invariant under multiplicative integers
• Disjointness in ergodic theory, minimal sets, and a problem in diophantine approximation

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