Periodic points, decidability and Markov subgroups

Abstract

We discuss the connections between the existence of periodic points and the question of determining whether or not a (ℤ or ℤ2) Markov shift is empty and whether or not a given admissible block occurs in a point. We prove that if the Markov shift has a group structure then the periodic points are dense. This implies that in this class the extension problem is decidable.KeywordsNormal SubgroupFinite GroupPeriodic PointFinite OrderInverse LimitThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.