2024/11/26 by Yifei Gu, Gu, Yifei, Jun Jie Miao +1 · 1 citation
Mathematics · Physics and Astronomy · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Theoretical and Computational Physics #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2411.17298
openalex publication_date 2024/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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≥ 1 .