Generalized $q$-dimensions of measures on nonautonomous fractals
Abstract
In the paper, we study the generalized -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 -dimensions of measures supported on nonautonomous attractors, and we provide dimension formulas for generalized -dimensions of measures supported on nonautonomous similar attractor under certain separation conditions. Next, we investigate the generalized -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 .
Keywords
Cite
@article{arxiv.2411.17298,
title = {Generalized $q$-dimensions of measures on nonautonomous fractals},
author = {Yifei Gu and Jun Jie Miao},
journal= {arXiv preprint arXiv:2411.17298},
year = {2024}
}
Comments
arXiv admin note: text overlap with arXiv:0911.0744 by other authors