Entropy and strict ergodicity for multidimensional Toeplitz subshifts

Abstract

In this work, we present a self-contained construction that proves the existence of strictly ergodic Toeplitz ${\mathbb{Z}}^d$-subshifts with arbitrary prescribed entropy. Moreover, any of these constructed subshifts will have the same maximal equicontinuous factor, which is the universal odometer over ${\mathbb{Z}}^d$.

Title changed; minor corrections and edits made; references updated. 25 pages, 3 figures