The degrees of onesided resolvingness and the limits of onesided resolving directions for endomorphisms and automorphisms of the shift

Abstract

We introduce the notions in the title for endomorphisms of subshifts, and using them we characterize various classes of "resolving endomorphisms of subshifts" in the broad sense including onesided and weak ones. Resolving endomorphisms of transitive topological Markov shifts and resolving automorphisms of topological Markov shifts are treated particularly in detail. Moreover, we understand what the limits of onesided resolving directions are for "expansiveness" (in the broad sense including onesided ones) of endomorphisms of subshifts, and we understand the relation between "resolvingness" and "expansiveness" for endomorphisms and automorphisms of subshifts and for Z^d-actions on zero-dimensional compact metric spaces.