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Prog. Theor. Phys. Vol. 64 No. 1 (1980) pp. 54-67

[ Full Text PDF : FREE ACCESS (1203K) ]

Chaos in Nonlinear Difference Equations. I

— Qualitative Study of (Formal) Chaos —

Yoshitsugu Oono and Motosige Osikawa*

Research Institute of Industrial Science, Kyushu University, Fukuoka 812
*Collete of General Education, Kyushu University, Fukuoka 810

(Received December 3, 1979)

Abstract:

The interrelations among physicists' intuitive pictures of chaos are considered. Fortunately, in the case of C0-endomorphisms of an interval (1-dimensional nonlinear difference equations with continuous functions), almost all the intuitively plausible pictures of chaos –the mixing property (of some induced map), the positivity of the Kolmogorov (and topological) entropy, the existence of a homoclinic point, the existence of some natural correspondence with the “coin-tossing” process (formal chaos), etc.–are equivalent. The chaos in the sense of Li and Yorke follows from one of these properties.


URL : http://ptp.ipap.jp/link?PTP/64/54/
DOI : 10.1143/PTP.64.54

[ Full Text PDF : FREE ACCESS (1203K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 63 No. 5 (1980) pp. 1804-1807 :
    Chaos, External Noise and Fredholm Theory
    Yoshitsugu Oono and Yoichiro Takahashi
  2. Progress of Theoretical Physics Vol. 71 No. 4 (1984) pp. 851-854 :
    Towards the Statistical Mechanics of Chaos
    Yoichiro Takahashi and Yoshitsugu Oono

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