Ergodic Theory and Dynamical Systems

Research Article

Textile systems and one-sided resolving automorphisms and endomorphisms of the shift

MASAKAZU NASUa1

a1 19-8, 9-chōme, Takaya-Takamigaoka, Higashi-Hiroshima 739-2115, Japan (email: nasu@quartz.ocn.ne.jp)

Abstract

Two results on textile systems are obtained. Using these we prove that for any automorphism φ of any topologically-transitive subshift of finite type, if φ is expansive and φ or φ−1 has memory zero or anticipation zero, then φ is topologically conjugate to a subshift of finite type. Moreover, this is generalized to a result on chain recurrent onto endomorphisms of topologically-transitive subshifts of finite type. Using textile systems and textile subsystems, we develop a structure theory concerning expansiveness with the pseudo orbit tracing property on directionally essentially weakly one-sided resolving automorphisms and endomorphisms of subshifts.

(Received September 05 2006)

(Revised April 30 2007)