Spectral Properties of a Piecewise Linear Intermittent Map |
| |
Authors: | S Tasaki P Gaspard |
| |
Institution: | (1) Advanced Institute for Complex Systems and Department of Applied Physics, School of Science and Engineering, Waseda University, 3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555, Japan;(2) Center of Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Campus Plaine C. P. 231, B-1050 Brussels, Belgium |
| |
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
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. |
| |
Keywords: | Generalized spectral decomposition generalized eigenfunctions intermittent map non-normalizable invariant measure |
本文献已被 SpringerLink 等数据库收录! |
|