AI Summary & Key Takeaways
AI InsightIn the present paper we introduce the variational principle for complexity for the $Z^2$ actions and prove the Kolmogorov assertion for continuous actions of $Z^2$.
📌 3 Key Takeaways
Abstract
The complexity of the finite object was introduced by A. Kolmogorov in [1] and it was conjectured that for the Z actions the complexity coincides with the topological entropy, [1], [2], [3]. In the present paper we introduce the variational principle for complexity for the $Z^2$ actions and prove the Kolmogorov assertion for continuous actions of $Z^2$.
Özet
Kolmogorow tarafından Z aksiyonları için komlekssiti ve topolojik entropiler sonlu nesneler için verilmiştir. Bizde bu çalışmada $Z^2$ için topolokik entropi ve komplekssitiyi tanımlayarak değişim prensibi ile ilişkisi incelenmektedir.