Study On Chaos And Sensitivity Via Furstenberg Family For Non-Autonomous Discrete Dynamical Systems


The respected Comrade Kim Jong Un said:

"The basic sciences are the cornerstone of a sci-tech power. A high level of basic sciences enables a country's science and technology to make steady progress on a solid foundation."

We studied the chaos and sensitivity via Furstenberg family for non-autonomous discrete dynamical systems given by a sequence of continuous surjections on compact metric space.

Over the last 40 years with the discovery of chaos lots of research have been done in autonomous dynamical systems. However, many complex systems occurring in the real world problems such as physical, biological and economic problems are necessarily described by non-autonomous dynamical systems.

It is more difficult to study dynamical behaviors of non-autonomous dynamical systems than those of autonomous dynamical systems in general. Therefore, there is a strong need to study and develop the theory of non-autonomous dynamical systems, which is more involved than autonomous dynamical systems.

Recently many mathematicians focused on complexity of non-autonomous dynamical systems and studied the chaotic properties of non-autonomous dynamical systems and applied many mathematical definitions of autonomous systems to non-autonomous systems.

We proved that the chaos via Furstenberg family is inherited under the kth iterations for a non-autonomous dynamical system which is constructed by a uniformly convergence sequence of continuous functions and so is the sensitivity via Fustenberg family. We generalized the result of previous work and answered positively for open question in previous work. In 2022, we submitted the obtained result in an article entitled "Inheritance of F-chaos and F-sensitivities under an iteration for non-autonomous discrete systems"( to the SCI journal "Discrete and Continuous Dynamical Systems-Series B" and it was published.