2021/09/24 by Yunping Wang, Wang, Yunping
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Boundary (topology) #Chaos control and synchronization #Combinatorics #Dimension (graph theory) #Dimension function #Dimension theory (algebra) #Dynamical Systems (math.DS) #Entropy (arrow of time) #FOS: Mathematics #Fractal dimension #Hausdorff dimension #Lebesgue covering dimension #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Metric (unit) #Minkowski–Bouligand dimension #Packing dimension #Physics #Pure mathematics #Topological entropy #Topological entropy in physics #Topological quantum number #Topological space #Topological vector space #Topology (electrical circuits) #Zero (linguistics) #Zero-dimensional space #math.DS
paper · pdf · doi:10.48550/arxiv.2109.11786
published in arXiv (Cornell University) (Cornell University)
arxiv created 2021/09/24 · openalex publication_date 2021/09/24 · arxiv updated 2021/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is devoted to the investigation of the weighted mean topological dimension in dynamical systems. We show that the weighted mean dimension is not larger than the weighted metric mean dimension, which generalizes the classical result of Lindenstrauss and Weiss \citeLWE. We also establish the relationship between the weighted mean dimension and the weighted topological entropy of dynamical systems, which indicates that each system with finite weighted topological entropy or small boundary property has zero weighted mean dimension.