L^q-spectra of box-like graph-directed self-affine measures: closed forms, with rotation

2023/09/12 by Qiu, Hua, Wang, Qi
#28A80 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.2309.05954

Abstract

We consider L^q-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 L^q-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 L^q-spectra of planar self-affine measures generated by diagonal matrices.

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