Generalized q-dimensions of measures on nonautonomous fractals
Abstract
In the paper, we study the generalized q-dimensions of measures supported by nonautonomous attractors, which are the generalization of classic Moran sets and attractors of iterated function systems. First, we estimate the generalized q-dimensions of measures supported on nonautonomous attractors, and we provide dimension formulas for generalized q-dimensions of measures supported on nonautonomous similar attractor under certain separation conditions. Next, we investigate the generalized q-dimensions of measures supported on nonautonomous affine sets and obtain the upper bounds. Finally, we study two variations of nonautonomous affine sets and obtain their dimension formulas for q≥ 1 .
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