Work

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

Year: 2025

Type: article

Abstract: For countably infinite IFSs on R 2 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.

Source: Nonlinearity

DOI: 10.1088/1361-6544/adbb4d

Authors: S van Golden, C Kalle, S Kombrink, T Samuel

Institutions: University of Birmingham, Leiden University, University of Exeter

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,325

Funders: University of Birmingham, Engineering and Physical Sciences Research Council