Publication

Ergodic Theory and Dynamical Systems

Paper

# Eventual factor maps and compositions of closing maps

## Abstract

We prove some results related to the question of the existence of factor maps and eventual factor maps between shifts of finite type. Our main result is that if A and B are integral eventually positive (IEP) matrices, and A eventually factors finite-to-one onto B, then there exists an IEP matrix C such that A eventually factors onto C by left closing maps and C eventually factors onto B by right closing maps. This answers the question of the existence of finite-to-one eventual factor maps when the spectrum of A is simple. As a corollary, if in addition to the above hypothesis, χA=χB, (where χA is the characteristic polynomial of A modulo x), then A is shift equivalent to B. © 1991, Cambridge University Press. All rights reserved.