Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions

Simone van Golden; C. Kalle; S. Kombrink; T. Samuel

doi:10.48550/arXiv.2404.10749

Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions

Simone van Golden, C. Kalle, S. Kombrink, T. Samuel^*

^*Corresponding author for this work

Mathematics

Research output: Contribution to journal › Article › peer-review

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Abstract

For countably infinite IFSs on R² consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower box-counting dimension. Moreover, we identify a family of countably infinite IFSs for which the Hausdorff and the affinity dimension are equal, and which have full dimension spectrum. The corresponding self-affine sets are related to restricted digit sets for signed Lüroth expansions.

Original language	English
Article number	045020
Number of pages	28
Journal	Nonlinearity
Volume	38
Issue number	4
DOIs	https://doi.org/10.48550/arXiv.2404.10749 https://doi.org/10.1088/1361-6544/adbb4d
Publication status	Published - 20 Mar 2025

Bibliographical note

Publisher Copyright:
© 2025 The Author(s). Published by IOP Publishing Ltd and the London Mathematical Society.

Keywords

affine iterated function system
Lüroth expansion
restricted digit set

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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vanGoldenS2025DimensionsFinal published version, 502 KBLicence: Creative Commons: Attribution (CC BY)

Complexity of random substitution tilings
Samuel, T. (Principal Investigator)
Engineering & Physical Science Research Council
1/11/23 → 31/08/24
Project: Research Councils

Cite this

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abstract = "For countably infinite IFSs on R2 consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower box-counting dimension. Moreover, we identify a family of countably infinite IFSs for which the Hausdorff and the affinity dimension are equal, and which have full dimension spectrum. The corresponding self-affine sets are related to restricted digit sets for signed L{\"u}roth expansions.",

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AU - Samuel, T.

PY - 2025/3/20

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N2 - For countably infinite IFSs on R2 consisting of affine contractions with diagonal linear parts, we give conditions under which the affinity dimension is an upper bound for the Hausdorff dimension and a lower bound for the lower box-counting dimension. Moreover, we identify a family of countably infinite IFSs for which the Hausdorff and the affinity dimension are equal, and which have full dimension spectrum. The corresponding self-affine sets are related to restricted digit sets for signed Lüroth expansions.

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KW - Lüroth expansion

KW - restricted digit set

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ER -

Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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Projects

Complexity of random substitution tilings

Cite this