Frequency-Domain Estimates for the Oscillation Periods of Nonlinear Discrete Systems

The method which can be used to estimate the oscillation periods of discrete control systems has been reported. Its application to various mappings gives estimates for the absence of oscillations of period 3. The method is based on the application of Fourier transforms as unitary operators in some function spaces. Therefore, quantitative scenarios of the transition to chaotic dynamics can be judged from nontrivial estimates for oscillation periods. Various equations and theorems have also been provided in support of the problem.