Non-commutative symbolic coding

Gohm, Rolf; Kummerer, B.; Lang, T., (2006) 'Non-commutative symbolic coding', Ergodic Theory and Dynamical Systems 26(5) pp.1521-1548 RAE2008

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.

Peer reviewed