Generalized $q$-dimensions of measures on nonautonomous fractals
| Autor: | Gu, Yifei, Miao, Jun Jie |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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 $. Comment: arXiv admin note: text overlap with arXiv:0911.0744 by other authors |
| Databáze: | arXiv |
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