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Prog. Theor. Phys. Vol. 68 No. 1 (1982) pp. 64-84

[ Full Text PDF : FREE ACCESS (864K) ]

Global Aspects of the Dissipative Dynamical Systems. I

— Statistical Identification and Fractal Properties of the Lorenz Chaos —

Yoji Aizawa

Department of Physics, University of Kyoto, Kyoto 606

(Received December 8, 1981)

Abstract:

Several empirical concepts which become practically necessary to characterize the ergodic motion in the dissipative systems are explained concretely by carrying out with the Lorenz model. Chaotic motions are characterized not only by the geometrical features in the phase space but also by the statistical aspects in the time series of the dynamical variables. These global aspects are understood in terms of the fractal properties appearing in the dimension spectrum of the strange attractor and the Hausdorff dimension of the time series. Furthermore, the internal stiffness and markovian order of the chaotic orbit are discussed in relation to the time series analysis based on the auto-regressive model. The numerical methods proposed here will be applied to the problem of the chaotic response under the periodic perturbation (in Part II).


URL : http://ptp.ipap.jp/link?PTP/68/64/
DOI : 10.1143/PTP.68.64

[ Full Text PDF : FREE ACCESS (864K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 64 (1995) pp. 1936-1944 :
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  2. Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1543-1560 :
    Some Routes to Chaos from Limit Cycle in the Forced Lorenz System
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  3. Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 1864-1879 :
    Global Aspects of the Dissipative Dynamical Systems. II
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  4. Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 333-337 :
    Intermittency Associated with the Breakdown of the Chaos Symmetry
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  5. Progress of Theoretical Physics Vol. 69 No. 5 (1983) pp. 1416-1426 :
    Generalization of Baker's Transformation
    Yoji Aizawa and Chikara Murakami
  6. Progress of Theoretical Physics Supplement No.79 (1984) pp. 96-124 :
    Statistical Mechanics of Intermittent Chaos
    Yoji Aizawa, Chikara Murakami and Tamotsu Kohyama

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