Spectral Properties of a Piecewise Linear Intermittent Map

For a piecewise linear intermittent map, 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 ^P are explicitly derived. The evolution of the averages are shown to be a superposition of the contributions from two simple eigenvalues 1 and λd∈(−1, 0), and a continuous spectrum on the unit interval [0,1] of ^P. Power-law decay of correlations are controlled by the continuous spectrum. Also the non-normalizable invariant measure in the non-stationary regime is shown to determine the strength of the power-law decay.