Abstract
We estimate the upper and lower Lq -spectra of measures generated by a class of graph-directed planar non-conformal iterated function systems. These systems are composed of C1+ϵ contractions with lower triangular pointwise Jacobian. The estimation provides a criterion for the existence of the Lq -spectra in certain case. As an application, we derive the box-counting dimension of planar self-affine sets generated by lower triangular matrices, whose geometric construction satisfies a finite overlapping type condition.
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