The Variational Principle and Complexity of Group Actions

The complexity of a finite object was introduced by A. Kolmogorow and V. Tihomirov in [1] and it was conjectured that for Z actions the complexity coincides with topological entropy [2]. In the present paper we introduce complexity for Z^n actions and prove the Kolmogorow assertion for continuous actions of Z. Then we study the variational principle and complexity for group actions.