$L^q$-spectra of box-like graph-directed self-affine measures: closed forms, with rotation
Classical Analysis and ODEs
2026-05-13 v1
Abstract
We consider -spectra of planar graph-directed self-affine measures generated by diagonal or anti-diagonal matrices. Assuming the directed graph is strongly connected and the system satisfies the rectangular open set condition, we obtain a general closed form expression for the -spectra. Consequently, we obtain a closed form expression for box dimensions of associated planar graph-directed box-like self-affine sets. We also provide a precise answer to a question of Fraser in 2016 concerning the -spectra of planar self-affine measures generated by diagonal matrices.
Keywords
Cite
@article{arxiv.2309.05954,
title = {$L^q$-spectra of box-like graph-directed self-affine measures: closed forms, with rotation},
author = {Hua Qiu and Qi Wang},
journal= {arXiv preprint arXiv:2309.05954},
year = {2026}
}
Comments
54 pages, 4 figures