Abstract
We investigate a class of dissipative flows which possess singular continuous (fractal) power spectra. The attractor for these flows contains a saddle point, so that the times between the returns of an orbit onto a secant plane are unbounded. As a result, the Poincaré map does not reflect precisely the qualitative dynamics of the underlying flow: the power spectrum of this map can be discrete. We introduce the construction which takes into account that the time intervals between the intersections of the Poincaré plane can vary and construct a symbolic representation for the continuous process with logarithmic divergence in the distribution of such intervals. Spectral properties of the resulting symbolic sequences are shown to reproduce rather well those of the original flow.
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