Spectral characterization of anomalous diffusion of a periodic piecewise linear intermittent map. (English) Zbl 1054.82015
Summary: 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 (FP) 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 Lévy flight if the reduced map is in the stationary regime with Lévy-type fluctuations and a transport of ballistic type if the reduced map is in the non-stationary regime.
MSC:
| 82C05 | Classical dynamic and nonequilibrium statistical mechanics (general) |
| 37C30 | Functional analytic techniques in dynamical systems; zeta functions, (Ruelle-Frobenius) transfer operators, etc. |
| 37E99 | Low-dimensional dynamical systems |
Keywords:
Generalized spectral decomposition; Generalized eigenfunctions; Intermittent map; Anomalous diffusion; Lévy flightReferences:
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