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arXiv · 1509.07858

Computable F{\o}lner monotilings and a theorem of Brudno I

Nikita Moriakov
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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 F{\o}lner 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.

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Nikita Moriakov. 2015-09-25. Computable F{\o}lner monotilings and a theorem of Brudno I. https://arxiv.org/abs/1509.07858

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