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) |