Ergodic Theory and Dynamical Systems

Research Article

Lower entropy factors of sofic systems

Mike Boylea1

a1 Department of Mathematics, University of Washington, Seattle, Washington 98195, USA

Abstract

A mixing subshift of finite type T is a factor of a sofic shift S of greater entropy if and only if the period of any periodic point of S is divisible by the period of some periodic point of T. Mixing sofic shifts T satisfying this theorem are characterized, as are those mixing sofic shifts for which Krieger's Embedding Theorem holds. These and other results rest on a general method for extending shift-commuting continuous maps into mixing subshifts of finite type.

(Received November 23 1982)

(Revised September 15 1983)