Upper metric mean dimensions with potential on subsets
Dandan Cheng, Zhiming Li, Bilel Selmi
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.
Topics & Concepts
MathematicsMetric (unit)Dimension (graph theory)Invariant (physics)Upper and lower boundsMetric spaceMeasure (data warehouse)Variational principleInverseMathematical analysisPure mathematicsGeometryMathematical physicsComputer scienceOperations managementDatabaseEconomicsMathematical Dynamics and FractalsAdvanced Topology and Set TheoryGeometric Analysis and Curvature Flows