Power Spectra of Strange Attractors

Abstract

It is shown that, for systems which enter chaos through period doubling bifurcations, the integrated noise power spectrum in the chaotic regime behaves as $N\left(\mathcal{r}\right)=N_0{(\mathcal{r}-{\mathcal{r}}_c)}^{\sigma }$, with $\sigma =1.5247\mathrm{}\dots$. Furthermore, the existence of a new universal constant which describes the scaling behavior of the average bandwidth in the strange attractor is reported. These results are directly applicable to experiments probing the onset of turbulence in physical systems.