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Computable symbolic dynamics

✍ Scribed by Douglas Cenzer; S. Ali Dashti; Jonathan L. F. King

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
149 KB
Volume
54
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Ξ ^0^~1~ class P is a subshift if and only if there exists a computable function F mapping 2^β„•^ to 2^β„•^ such that P is the set of itineraries of elements of 2^β„•^. Ξ ^0^~1~ subshifts are constructed in 2^β„•^ and in 2^β„€^ which have no computable elements. We also consider the symbolic dynamics of maps on the unit interval. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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