TY - UNPB
T1 - Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions
AU - Van Dijk, Sven
AU - Kalle, Charlene
AU - Kombrink, Sabrina
AU - Samuel, Tony
N1 - 16 pages, 1 figure with 3 subfigures.
PY - 2024/4/16
Y1 - 2024/4/16
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 affinity dimension are equal, and which have full dimension spectrum. The corresponding self-affine sets are related to restricted digit sets for signed L\"uroth expansions.
AB - 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 affinity dimension are equal, and which have full dimension spectrum. The corresponding self-affine sets are related to restricted digit sets for signed L\"uroth expansions.
U2 - 10.48550/arXiv.2404.10749
DO - 10.48550/arXiv.2404.10749
M3 - Preprint
BT - Dimensions of infinitely generated self-affine sets and restricted digit sets for signed Lüroth expansions
PB - arXiv
ER -