Subshifts with sparse traces

Abstract

We study two-dimensional subshifts whose horizontal trace (also called projective subdynamics) contains only configurations of finite support. Our main result is a classification result for such subshifts satisfying a minimality property. As corollaries, we obtain new proofs for various known results on traces of SFTs, nilpotency, and decidability results for cellular automata and topological full groups. We also construct various (sofic) examples illustrating the concepts.