Generalized $q$-dimensions of measures on nonautonomous fractals
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910716560146432 |
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| author | Gu, Yifei Miao, Jun Jie |
| author_facet | Gu, Yifei Miao, Jun Jie |
| contents | 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 $. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalized $q$-dimensions of measures on nonautonomous fractals Gu, Yifei Miao, Jun Jie Dynamical Systems Classical Analysis and ODEs 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 $. |
| title | Generalized $q$-dimensions of measures on nonautonomous fractals |
| topic | Dynamical Systems Classical Analysis and ODEs |
| url | https://arxiv.org/abs/2411.17298 |