Power Spectra of Strange Attractors

It is shown that, for systems which enter chaos through period doubling bifurcations, the integrated noise power spectrum in the chaotic regime behaves as N(r) =N ₀(r − r_c )^σ, with σ = 1.5247… . Furthermore, the existence of a new universal constant which de- scribes the scaling behavior of the average bandwidth in the strange attractor is re- ported. These results are directly applicable to experiments probing the onset of tur- bulence in physical systems.