REMARK ON THE LOCAL NATURE OF METRIC MEAN DIMENSION

Abstract

Metric mean dimension is a metric invariant of dynamical systems. It is a dynamical analogue of Minkowski dimension of metric spaces. We use old ideas of Bowen (Trans. Amer. Math. Soc. 164 (1972), 323-331) for clarifying the local nature of metric mean dimension. We also generalize the local formula to metric mean dimension of ℝ^D-action dynamics and apply the result to simplify a previous proof of the mean dimension estimate of the ℂ-action on the space of Brody curves.