TY - JOUR

T1 - Time correlation calculation method based on delayed coordinates

AU - Morino, Kai

AU - Kobayashi, Miki U.

AU - Mlyazaki, Syuji

PY - 2009/6

Y1 - 2009/6

N2 - An approximate calculation method of time correlations by use of delayed coordinate is proposed. For a solvable piecewise linear hyperbolic chaotic map, this approximation is compared with the exact calculation, and an exponential convergence for the maximum time delay M is found. By use of this exponential convergence, the exact result for M → ∞ is extrapolated from this approximation for the first few values of M. This extrapolation is shown to be much better than direct numerical simulations based on the definition of the time correlation function. As an application, the irregular dependence of diffusion coefficients similar to Takagi or Weierstrass functions is obtained from this approximation, which is indistinguishable from the exact result only at M = 2. The method is also applied to the dissipative Lozi and Hénon maps and the conservative standard map in order to show wide applicability.

AB - An approximate calculation method of time correlations by use of delayed coordinate is proposed. For a solvable piecewise linear hyperbolic chaotic map, this approximation is compared with the exact calculation, and an exponential convergence for the maximum time delay M is found. By use of this exponential convergence, the exact result for M → ∞ is extrapolated from this approximation for the first few values of M. This extrapolation is shown to be much better than direct numerical simulations based on the definition of the time correlation function. As an application, the irregular dependence of diffusion coefficients similar to Takagi or Weierstrass functions is obtained from this approximation, which is indistinguishable from the exact result only at M = 2. The method is also applied to the dissipative Lozi and Hénon maps and the conservative standard map in order to show wide applicability.

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U2 - 10.1143/PTP.121.1143

DO - 10.1143/PTP.121.1143

M3 - Article

AN - SCOPUS:70349682922

VL - 121

SP - 1143

EP - 1156

JO - Progress of Theoretical Physics

JF - Progress of Theoretical Physics

SN - 0033-068X

IS - 6

ER -