a1 IBM, Thomas J. Watson Research Center, P.O. Box 218, Yorktown Heights, New York 10598, USA and Mathematical Sciences Research Institute, 2223 Fulton Street, Room 603, Berkeley, CA 94720, USA
Only finitely many shift equivalence classes of non-negative aperiodic integral matrices may share a given diagonal Jordan form away from zero. The diagonal assumption is necessary.
(Received March 13 1984)