The phase of a chaotic trajectory in autonomous flows is often ignored because of the wide use of the extremely popular Poincar\'e surface-of-section technique in the study of chaotic systems. We present evidence that, in general, a chaotic flow is practically composed of a small number of intrinsic modes of proper rotations from which the phase can be computed via the Hilbert transform. The fluctuations of the phase about that of a uniform rotation can be described by fractional Brownian random processes. Implications to nonlinear digital communications are pointed out.
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Yalçınkaya et al. (1997) studied this question.
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