Slow Metric Mean Dimensions for Dynamical Systems

We introduce slow metric mean dimensions, a new family of invariants for dynamical systems with subexponential growth complexity. For the exponential scale a_χ (n)=e^χ n , these invariants are shown to coincide with classical metric mean dimensions. We establish fundamental inequalities relating their measure-theoretic, Katok, and topological versions.Under an additional homogeneity assumption on the invariant measure, we obtain an equality linking the topological slow metric mean dimension to a pointwise Bowen-ball growth rate.