Non-commutative symbolic coding

Rolf Gohm; Burkhard Kuemmerer; Tatjana Lang

doi:10.1017/S0143385706000332

Non-commutative symbolic coding

Rolf Gohm, Burkhard Kuemmerer, Tatjana Lang

Department of Physics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1521-1548
Number of pages	28
Journal	Ergodic Theory and Dynamical Systems
Volume	26
Issue number	5
Early online date	11 Sept 2006
DOIs	https://doi.org/10.1017/S0143385706000332
Publication status	Published - 01 Oct 2006

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AB - 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.

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Non-commutative symbolic coding

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