Computable symbolic dynamics

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Abstract

We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π01 class P is a subshift if and only if there exists a computable function F mapping 2 to 2 such that P is the set of itineraries of elements of 2. Π01 subshifts are constructed in 2 and in 2 which have no computable elements. We also consider the symbolic dynamics of maps on the unit interval. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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