Fluctuation spectra of Few-and Large-degree-of-freedom Chaotic Systems

Abstract

Following Fujisaka's basic idea, large deviation statistics characterizing temporal fluctuations are calculated based on Mori's projection-operator method. It is shown that this calculation will overcome the finite-sample effect studied by Nakao et al. due to the finiteness of the length of time series, of the time span of the local average, or of the ensemble of numerical data. The proposed method are compared with direct numerical simulations using analytically solvable chaotic maps, and a much wider range of large deviation is observed far beyond the finite-sample direct numerical simulations.