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arXiv · 2411.17298

Generalized $q$-dimensions of measures on nonautonomous fractals

Yifei Gu·Jun Jie Miao
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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\geq 1 $.

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Yifei Gu, Jun Jie Miao. 2024-11-26. Generalized $q$-dimensions of measures on nonautonomous fractals. https://arxiv.org/abs/2411.17298

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