Abstract
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 λ d ∈(−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.
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Tasaki, S., Gaspard, P. Spectral Properties of a Piecewise Linear Intermittent Map. Journal of Statistical Physics 109, 803–820 (2002). https://doi.org/10.1023/A:1020479002249
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DOI: https://doi.org/10.1023/A:1020479002249