Real and apparent divergencies in low-frequency spectra of nonlinear dynamical systems

Abstract

We discuss apparent and real 1/$f^{\delta }$ divergencies in the small-frequency limit of power spectra of dynamical systems. Apparent 1/$f^2$ divergencies appear in ‘‘type-I’’ intermittency and whenever there is infrequent random hopping between regions with chaotic motion. Real 1/$f^{\delta }$ divergencies appear in ‘‘types-II and -III’’ intermittency. The universal properties of these divergencies are discussed in the context of one- and two-dimensional maps.