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Prog. Theor. Phys. Vol. 67 No. 3 (1982) pp. 982-985

[ Full Text PDF : FREE ACCESS (177K) ]

Letters

Topological Aspects in Chaos and in 2k-Period Doubling Cascade

Yoji Aizawa and Tatsuya Uezu

Department of Physics, Kyoto University, Kyoto 606

(Received November 30, 1981)

Abstract:

Several parameters which characterize the topoligical features of chaos and limit cycle are proposed and these are applied to the analysis of the global behaviours in the forced Lorenz system.


URL : http://ptp.ipap.jp/link?PTP/67/982/
DOI : 10.1143/PTP.67.982

[ Full Text PDF : FREE ACCESS (177K) ] Citation:

References:

  1. Y. Aizawa, RIMS Kokyuroku (Symposium on Random systems and Dynamical systems, Research Institute for Math. Sci., Kyoto University) 439 (1981), 63.
  2. I. Fáry, Bull. Soc. Math. France 77 (1949), 128.
  3. J. Milnor, Math. Scand. 1 (1953), 289.
  4. C. F. Gauss, Zur mathematischen Theorie der electrodynamischen Wirkungen, vol. 5, (Werke, Königlichen Gesellschaft der Wissenchaften zu Göttingen, 1877).
  5. M. J. Feigenbaum, J. Stat. Phys. 21 (1979), 669[CrossRef].

Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1543-1560 :
    Some Routes to Chaos from Limit Cycle in the Forced Lorenz System
    Tatsuya Uezu and Yoji Aizawa
  2. Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 1864-1879 :
    Global Aspects of the Dissipative Dynamical Systems. II
    Yoji Aizawa and Tatsuya Uezu
  3. Progress of Theoretical Physics Vol. 68 No. 6 (1982) pp. 1907-1916 :
    Topological Character of a Periodic Solution in Three-Dimensional Ordinary Differential Equation System
    Tatsuya Uezu and Yoji Aizawa
  4. Progress of Theoretical Physics Vol. 69 No. 5 (1983) pp. 1416-1426 :
    Generalization of Baker's Transformation
    Yoji Aizawa and Chikara Murakami
  5. Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1249-1263 :
    Symbolic Dynamics Approach to Intermittent Chaos
    Yoji Aizawa
  6. Progress of Theoretical Physics Vol. 83 No. 5 (1990) pp. 850-874 :
    Topological Structure in Flow Systems
    Tatsuya Uezu
  7. Progress of Theoretical Physics Vol. 93 No. 6 (1995) pp. 1135-1140 :
    On the Topological Aspect in General-Dimensional Dynamical Systems
    Tatsuya Uezu and Hirotsugu Kubo

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