On α-chaotic points and chaotic (antichaotic) families of functions.

In this paper, a new definition of the entropy of functions and α-entropy points (α≥1) will be introduced. These concepts will be used to explore the possibility of internal disruptions (introducing a virus in the phase space) in order to receive an α-chaotic point.

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 the local aspects of distributional chaos.

In this paper, the notion of a distributionally chaotic point (connected with focusing of an uncountable distributionally scrambled set and its envelope around this point) is introduced. The theorems dealing with the existence of such points for selfmaps of the closed unit interval and the possibilities of approximation of nonautonomous discrete dynamical systems by systems with i-stable and p-DC1 points are proved.

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.