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

摘要

Two results on textile systems are obtained. Using these we prove that for any automorphism phi of any topologically-transitive subshift of finite type, if phi is expansive and phi or phi(-1) has memory zero or anticipation zero, then phi 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.