Renormalization of correlations and spectra of a strange non-chaotic attractor

We study a simple nonlinear mapping with a strange nonchaotic attractor characterized by a singular continuous power spectrum. We show that the symbolic dynamics is exactly described by a language generated from a suitable inflation rule. We derive renormalization transformations for both the power spectrum and the autocorrelation function, thus obtaining a quantitative description of the scaling properties. The multifractal nature of the spectrum is also discussed.