Upper metric mean dimensions with potential on subsets. (27th January 2021)

• Record Type: Journal Article
• Authors: Cheng, Dandan; Li, Zhiming; Selmi, Bilel
• Is Part Of: Nonlinearity. Volume 34:Number 2(2021)
• Page Start: 852
• Page End: 867
• Publication Date: 2021-01-27
• Subjects: weighted upper mean dimension -- variational principle -- inverse variational principle; 58F11 -- 58F15; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/abcd08
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we introduce the notion of upper metric mean dimension with potential on any subset (not necessarily compact or invariant) via Carathéodory–Pesin structures. We discuss several possible versions of upper measure-theoretic mean dimensions with potential and find conditions to make these notions coincide. In particular, we present a corresponding variational principle and an inverse variational principle.