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Computable symbolic dynamics. (English) Zbl 1170.03029
The paper mainly consider computable dynamical systems on the string space \(\{0,1,\dots,k\}^{\mathbb N}\). The symbolic dynamics relative to a clopen partition is considered and several results are proved on the associated subshift. In particular, this set is proved to be an effectively closed set, and examples of \(\Pi _0^1 \) subshifts without computable elements are contructed. In the last part of the paper this framework is applied to investigate some computability question about unimodal maps and their symbolic dynamics.

03F60 Constructive and recursive analysis
03D80 Applications of computability and recursion theory
26E40 Constructive real analysis
37B10 Symbolic dynamics
Full Text: DOI
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