Resolving factor maps for shifts of finite type with equal entropy

Abstract

Abstract We sharpen a result of Boyle, Marcus and Trow as follows. An aperiodic shift of finite type Σ A factors onto another Σ B with equal entropy by a 1-to-l almost everywhere right-closing map if and only if (1) the dimension group for Σ B is a quotient of that for Σ A ; and (2) Σ A and Σ B satisfy the trivial periodic point condition for existence of a shift-commuting map from Σ A to Σ B .