STRUCTURE ANALYSIS OF FRACTAL AND CHAOTIC COMPONENTS OF CYCLIC TRAJECTORIES FOR CONGRUENT NONLINEAR DYNAMICAL MAPS

STRUCTURE ANALYSIS OF FRACTAL AND CHAOTIC COMPONENTS OF CYCLIC

TRAJECTORIES FOR CONGRUENT NONLINEAR DYNAMICAL MAPS

 

  1. Vostrov, A. Khrinenko

State University «Odessa Polytechnic»

 

Abstract. In this paper we consider the processes in maps, which are examples of nonlinear dynamical systems. Analyzing 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.

Key words: dynamical systems, nonlinear maps, randomness, trajectories, chaotic processes.