Spectral Characterization of Anomalous Diffusion of a Periodic Piecewise Linear Intermittent Map

For a piecewise linear version of the periodic map with anomalous diffusion, the evolution of statistical averages of a class of observables with respect to piecewise constant initial densities is investigated and generalized eigenfunctions of the Frobenius-Perron operator are explicitly derived. The evolution of the averages is controlled by real eigenvalues as well as continuous spectra terminating at the unit circle. Appropriate scaling limits are shown to give a normal diffusion if the reduced map is in the stationary regime with normal fluctuations, a L\'evy flight if the reduced map is in the stationary regime with L\'evy-type fluctuations and a transport of ballistic type if the reduced map is in the non-stationary regime.