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

Published online by Cambridge University Press:  01 February 2008

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

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Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 1 , February 2008 , pp. 167 - 209
Copyright
Copyright © Cambridge University Press 2007

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