On Entropy-Like Invariants for Dynamical Systems

Abstract

This paper transfers the theory of the Kolmogorov-Sinai-entropy a method which is a basic tool in the theory of the order-structure of states. The function $h(x)=—x$ log $z$ is replaced by arbitrary bounded, concave functions in all definitions of the entropy-theory. This procedure leads to a class of isomorphy invariants, thus generalizing the notion of dynamical entropy. The general properties of the generalized dynamical entropies are investigated and an explicit calculation of the new invariants is accomplished on some simple cases.