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Non-commutative symbolic coding

Published online by Cambridge University Press:  11 September 2006

ROLF GOHM ,
BURKHARD KÜMMERER  and
TATJANA LANG
ROLF GOHM
Affiliation:
Department of Mathematics, University of Reading, PO Box 220, Berkshire, Reading RG6 6AX, UK (e-mail: [email protected])
BURKHARD KÜMMERER
Affiliation:
Fachbereich Mathematik, Technische Universität Darmstadt, Schloßgartenstr. 7, 64289 Darmstadt, Germany (e-mail: [email protected])
TATJANA LANG
Affiliation:
Universität Stuttgart, Mathematisches Institut A, Pfaffenwaldring 57, 70569 Stuttgart, Germany (e-mail: [email protected])
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Abstract

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 26 , Issue 5 , October 2006 , pp. 1521 - 1548
Copyright
2006 Cambridge University Press

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