English

Generalized $q$-dimensions of measures on nonautonomous fractals

Dynamical Systems 2024-11-27 v1 Classical Analysis and ODEs

Abstract

In the paper, we study the generalized qq-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 qq-dimensions of measures supported on nonautonomous attractors, and we provide dimension formulas for generalized qq-dimensions of measures supported on nonautonomous similar attractor under certain separation conditions. Next, we investigate the generalized qq-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 q1q\geq 1 .

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