Measuring chaos by entropy for a finite family of functions.

In this paper, we consider chaos of a finite family of continuous functions. As a measure of chaos, we use three types of entropies defined for that family. The first type of entropy is connected with the entropy of semigroups while the second and the third type concern entropy of nonautonomous dynamical systems.

On Points Focusing Entropy.

In the paper, we consider local aspects of the entropy of nonautonomous dynamical systems. For this purpose, we introduce the notion of a (asymptotical) focal entropy point. The notion of entropy appeared as a result of practical needs concerning thermodynamics and the problem of information flow, and it is connected with the complexity of a system.