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 P̂ 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 P̂ . Power-law decay of correlations are controlled by the continuous spectrum. Also the non-normalizable invariant measure in the nonstationary regime is shown to determine the strength of the power-law decay.