Bowen’s Equations for Weighted Upper Metric Mean Dimension with Potential

Abstract

In this paper, we define the weighted upper metric mean dimension with potential and derive its corresponding Bowen’s equation. Furthermore, we introduce the weighted BS metric mean dimension and the weighted packing BS metric mean dimension on the subsets, and prove Bowen’s equations for both. Additionally, we establish variational principles for these dimensions, linking them to the weighted local measure-theoretic entropy.

Keywords

• variational principle
• Bowen’s equation
• weighted metric mean dimension with potential