Non-commutative symbolic coding

Gohm, R., Kummerer, B. and Lang, T. (2006) Non-commutative symbolic coding. Ergodic Theory and Dynamical Systems, 26. pp. 1521-1548. ISSN 0143-3857

Abstract/Summary

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.