Methods and Approaches for Behavior Analysis of Fractal and Chaotic Components of Cyclic Trajectories of Nonlinear Dynamical Systems

Abstract

This paper considers the processes in maps, which are examples of nonlinear dynamical systems. Analysing dynamical systems, it is necessary to take into account and analyze properties of iterative functions that determine the length of nonrepetitive iterative process. It is shown that not only properties of functions, but also properties of numbers from the considered functions domain influence the nonlinear maps behavior.