On the Relation between the Average Complexity Oftrajectorries and the Complexity for Z^n Actions
The complexity of finite object was introduced by A. Kolmogorov and V. Tihomirov in (, , ) and it was conjectured that for Z actions complexity coincides with topological entropy, (, , ). In the present paper we introduce complexity for Z^n actions and prove the Kolmogorov assertion for continuous actions of Z^n(, ). After, We will examine the relation between the average complexity of trajectories and the complexity for Z^nactions.
Dynamical System, Configuration Spaces, Complexity, Topological Entropy, Measure-Preserving Transformations, Algorithmic, Convergence Rates
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