Computable Følner monotilings and a theorem of Brudno I

2015/09/25 by Nikita Moriakov, Moriakov, Nikita · 1 citation
Computer Science · Mathematics · #03D15 #37B10 #37B40 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1509.07858

openalex publication_date 2015/09/25 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The purpose of this article is to extend the earliest results of A.A. Brudno, connecting topological entropy of a subshift X over 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 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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