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

TL;DR

This paper introduces new notions of resolvingness for endomorphisms of subshifts, characterizes classes of resolving endomorphisms, and explores the limits of resolving directions related to expansiveness and their relations.

Contribution

It defines and characterizes various classes of resolving endomorphisms and automorphisms of subshifts, including onesided and weak types, and analyzes the limits of resolving directions in relation to expansiveness.

Findings

Characterization of resolving endomorphisms of transitive topological Markov shifts.

Analysis of limits of onesided resolving directions for expansiveness.

Relations between resolvingness and expansiveness for subshift endomorphisms and automorphisms.

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.