Time Correlation Calculation Method Based on Delayed Coordinates
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- Morino Kai MORINO Kai
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
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- Kobayashi Miki U. KOBAYASHI Miki U.
- Research Institute for Mathematical Sciences, Kyoto University
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- Miyazaki Syuji MIYAZAKI Syuji
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
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Author(s)
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- Morino Kai MORINO Kai
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
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- Kobayashi Miki U. KOBAYASHI Miki U.
- Research Institute for Mathematical Sciences, Kyoto University
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- Miyazaki Syuji MIYAZAKI Syuji
- Department of Applied Analysis and Complex Dynamical Systems, Graduate School of Informatics, Kyoto University
Abstract
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.
Journal
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- Progress of Theoretical Physics
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Progress of Theoretical Physics 121(6), 1143-1156, 2009-06-25
Oxford University Press (OUP)
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