Computable Følner monotilings and a theorem of Brudno I

Abstract

The purpose of this article is to extend the earliest results of A.A. Brudno, connecting topological entropy of a subshift X over $\mathbb{N}$ to the Kolmogorov complexity of words in X, to subshifts over computable groups that posses computable Følner monotilings, which we introduce in this work. The classical examples of such groups are the groups ${\mathbb{Z}}^d$ and the groups of upper-triangular matrices with integer entries. Following the work of B. Weiss we show that the class of such groups is closed under group extensions.

14 pages; corrections in Thm. 3.3

References in corpus (1)

• A Banach space-valued ergodic theorem and the uniform approximation of the integrated density of states

Cited by in corpus (1)

• Kolmogorov complexity and entropy of amenable group actions