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An invariant for bounded-to-one factor maps between transitive sofic subshifts

Published online by Cambridge University Press:  19 September 2008

Masakazu Nasu
Masakazu Nasu
Affiliation:
Faculty of Engineering, Mie University, Tsu 514, Japan
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Abstract

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We define a ‘core-matrix’ of a transitive sofic subshift, which is unique up to similarity for each transitive sofic subshift. We prove that if there exists a bounded-to-one factor map from one transitive sofic subshift to another, the block of the Jordan form of a core-matrix of this second subshift with non-zero eigenvalues is a principal submatrix of the Jordan form of a core-matrix of the first. We also prove that the subshifts that are almost of finite type are ‘spectrally of finite type’.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 5 , Issue 1 , March 1985 , pp. 89 - 105
Copyright
Copyright © Cambridge University Press 1985

References

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