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Orbit complexity by computable structures. (English) Zbl 0996.37012

Summary: We give a definition of orbit complexity for points in topological systems over separable metric spaces. Our definition extends Brudno’s definition meaningfully to the non-compact case. Interacting with constructive mathematics we investigate questions about orbit complexity from a new point of view. In particular, we show a relation between constructivity, entropy and orbit complexity.

MSC:

37B10 Symbolic dynamics
68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)
37B40 Topological entropy
28D15 General groups of measure-preserving transformations
03D15 Complexity of computation (including implicit computational complexity)
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