Existence of an infinite-dimensional mmd-expansive subshift

Construct an infinite-dimensional subshift of the shift map on the Hilbert cube that is mmd-expansive.

Background

The paper defines mmd-expansiveness using the vanishing of metric mean dimension on sufficiently small dynamical Bowen balls. It then shows that the full shift on the infinite-dimensional Hilbert cube is not even lower mmd-expansive, because arbitrarily small Bowen balls contain invariant products whose lower metric mean dimension is at least one.

The unresolved question asks whether an appropriate infinite-dimensional subshift—presumably a suitably chosen invariant subsystem of the Hilbert-cube shift—can nevertheless satisfy mmd-expansiveness, providing an example with the desired property despite the failure for the full shift.