Power Spectra and Mixing Properties of Strange Attractors

Abstract:

We have found that, to the resolution of our numerical experiments, some strange attractors have power spectra that are superpositions of delta functions and broad backgrounds. As we shall show, strange attractors with this property, which we call phase coherence, are chaotic, yet, nonetheless. at least approach being periodic or quasi-periodic in a statistical sense. Under various names, this property has also been noted by Lorenz (“noisy peri~dicity”),I~to et al. (“nonmixing ~haos”),a~nd the authors6 The existence of phase coherence can make it difficult to discriminate experimentally between chaotic and periodic behavior by means of a power spectrum. In this paper, we investigate the geometric basis of phase coherence and demonstrate that this phenomenon is closely related to the mixing properties of attractors.