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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.

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