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Eventual factor maps and compositions of closing maps

Published online by Cambridge University Press:  19 September 2008

Bruce Kitchens ,
Brian Marcus  and
Paul Trow
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
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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
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 1 , March 1991 , pp. 85 - 113
Copyright
Copyright © Cambridge University Press 1991

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