Strictly ergodic Toeplitz $\mathbb{Z}^d$-subshifts with arbitrary entropy

TL;DR

This paper constructs strictly ergodic Toeplitz $ abla$-subshifts with any specified entropy, demonstrating their existence and shared maximal equicontinuous factors, advancing understanding of dynamical systems with prescribed entropy.

Contribution

It provides a comprehensive construction method for strictly ergodic Toeplitz $ abla$-subshifts with arbitrary entropy, showing their existence and common maximal equicontinuous factors.

Findings

Existence of strictly ergodic Toeplitz $ abla$-subshifts with any entropy

All constructed subshifts share the same maximal equicontinuous factor

The construction broadens understanding of entropy in dynamical systems

Abstract

In this work, we present a comprehensive construction that proves the existence of strictly ergodic Toeplitz $\mathbb{Z}^d$-subshifts which admit arbitrary given entropy. Moreover, any of these constructed subshifts will have the same maximal equicontinuous factor.