Time correlation calculation method based on delayed coordinates

Kai Morino, Miki U. Kobayashi, Syuji Mlyazaki

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    1 Citation (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)1143-1156
    Number of pages14
    JournalProgress of Theoretical Physics
    Issue number6
    Publication statusPublished - 2009 Jun

    ASJC Scopus subject areas

    • Physics and Astronomy (miscellaneous)


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