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Prog. Theor. Phys. Vol. 62 No. 1 (1979) pp. 61-69

[ Full Text PDF : FREE ACCESS (677K) ]

Gibbsian Distribution on the Lorenz Attractor

Ippei Shimada

Department of Physics, Hokkaido University, Sapporo 060

(Received January 20, 1979)

Abstract:

A representation of the Lorentz attractor by a 1-dimensional Ising system is constructed. Gibbsian distribution function which describes the irregular motion of this dissipative dynamical system is investigated with the help of this representation. Relation between measure-theoretical entropy and positive Lyapunov characteristic exponent is also investigated. The following conclusions are obtained: (1) The statistical properties of the Lorenz system can be reduced to those of 1-dimensional Ising system with short-range interaction, in other words, the time correlation function of the Lorenz system shows no singular long-time behaviour. (2) The positive Lyapunov characteristic exponent of the Lorenz system is almost equal to its measure-theoretical entropy.


URL : http://ptp.ipap.jp/link?PTP/62/61/
DOI : 10.1143/PTP.62.61

[ Full Text PDF : FREE ACCESS (677K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 63 No. 1 (1980) pp. 91-105 :
    Dynamics of the Lorenz Model of Convective Instabilities. II
    Kyôzô Takeyama
  2. Progress of Theoretical Physics Vol. 64 No. 5 (1980) pp. 1532-1550 :
    Statistical Mechanics of Deterministic Chaos
    Tohru Kai and Kazuhisa Tomita
  3. Progress of Theoretical Physics Vol. 68 No. 1 (1982) pp. 64-84 :
    Global Aspects of the Dissipative Dynamical Systems. I
    Yoji Aizawa
  4. Progress of Theoretical Physics Supplement No.69 (1980) pp. 185-199 :
    Towards the Interpretation of the Global Bifurcation Structure of the Lorenz System
    Kazuhisa Tomita and Ichiro Tsuda
  5. Progress of Theoretical Physics Supplement No.99 (1989) pp. 107-119 :
    Optimized Statistical Model for Lorenz System
    Ippei Shimada and Tatsuo Yanagita

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