Conjugacy of $Z^2$-subshifts and Textile Systems

Abstract

It will be shown that any topological conjugacy of $Z^2$-subshifts is factorized into a finite number of bipartite codes, and that in particular when textile shifts which are $Z^2$-subshifts arising from textile systems introduced by Nasu are taken each bipartite code appearing in this factorization is given by a bipartite graph code of textile shifts which is defined in terms of textile systems. The latter result extends the Williams result on strong shift equivalence of $Z^1$-topological Markov shifts to a $Z^2$-shift case.