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Eventual factor maps and compositions of closing maps

Published online by Cambridge University Press:  19 September 2008

Bruce Kitchens
Affiliation:
IBM Research, T.J. Watson Research Center, Yorktown Heights, New York 10598, USA
Brian Marcus
Affiliation:
IBM Research, Almaden Research Center, 650 Harry Road, San Jose, California 95120, USA
Paul Trow
Affiliation:
Mathematics Department, University of California Berkeley, Berkeley, California 94720, USA

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, χ*A=χ*B, (where χ*A is the characteristic polynomial of A modulo x), then A is shift equivalent to B.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1991

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