Bowen's equations for upper metric mean dimension with potential. (1st September 2022)

• Record Type: Journal Article
• Authors: Yang, Rui; Chen, Ercai; Zhou, Xiaoyao
• Is Part Of: Nonlinearity. Volume 35:Number 9(2022)
• Page Start: 4905
• Page End: 4938
• Publication Date: 2022-09-01
• Subjects: variational principle -- upper metric mean dimension with potential -- Bowen's equation -- generic points; 58F11 -- 58F15; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac8265
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: Firstly, we introduce a new notion called induced upper metric mean dimension with potential, which naturally generalises the definition of upper metric mean dimension with potential given by Tsukamoto to more general cases, then we establish variational principles for it in terms of upper and lower rate distortion dimensions and show there exists a Bowen's equation between induced upper metric mean dimension with potential and upper metric mean dimension with potential. Secondly, we continue to introduce two new notions, called BS metric mean dimension and packing BS metric mean dimension on arbitrary subsets, to establish Bowen's equations for Bowen upper metric mean dimension and packing upper metric mean dimension with potential on subsets. Besides, we also obtain two variational principles for BS metric mean dimension and packing BS metric mean dimension on subsets. Finally, the special interest about the Bowen upper metric mean dimension of the set of generic points of ergodic measures are also involved.