Properties of Fourier spectrum of the signal , generated at the accumulation point of period - tripling bifurcations

Universal regularities of the Fourier spectrum of signal, generated by complex analytic map at the period-tripling bifurcations accumulation point are considered. The difference between intensities of the subharmonics at the values of frequency corresponding to the neighbor hierarchical levels of the spectrum is characterized by a constant γ = 21.9 dB?, which is an analogue of the known value γF = 13.4 dB, intrinsic to the Feigenbaum critical point. Data of the physical experiment, directed to the observation of the spectrum at period-tripling accumulation point, are represented. One of the simplest objects, demonstrating non-trivial dynamics, is the system with discrete time, defined by the quadratic map. In particular, the period-doubling bifurcations cascade, characterized by the universal Feigenbaum properties, occures in this system [1]. By generalization to the case of complex variable the quadratic map zn+1 = λ− z 2 n , λ, z ∈ C (1)