On Variational Principles for Metric Mean Dimension
Ruxi Shi
Abstract
In this note, we show several variational principles for metric mean dimension. First we prove a variational principles in terms of Shapira’s entropy related to finite open covers. Second we establish a variational principle in terms of Katok’s entropy. Finally using these two variational principles we develop a variational principle in terms of Brin-Katok local entropy.
Topics & Concepts
MathematicsVariational principleEntropy (arrow of time)Dimension (graph theory)Variational analysisApplied mathematicsMetric (unit)Variational methodMathematical analysisPure mathematicsPhysicsEconomicsOperations managementQuantum mechanicsMathematical Dynamics and FractalsAdvanced Numerical Analysis TechniquesGeometric Analysis and Curvature Flows