Analytic Properties of Characteristic Exponents for Chaotic Dynamical Systems : General and Mathematical Physics
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概要
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A study on an analogy in mathematical formalism between a characteristic exponent λ_p=(1/q) lim_<j→∞> (1/j)ln<exp(qΣ^<j-1>_<s=0>Δ_s)>, where {Δ_j} is a steady one-dimensional time sequence, and other functions such as the Helmholtz free energy and a set of dimensions of a strange attractor, is carried out, and a new concept "filtering parameter" is proposed. The inverse temperature acts as the filtering parameter in the Helmholtz free energy. A complex partition function Z(z)=exp(zλ_z) is introduced in order to classify chaos transitions. Distribution of the solutions of Z(s)=0 is calculated for several time sequences which are generated by chaotic dynamical systems. It is found that there are two types of transitions;(a) the solutions accumulate at the north pole of Riemann sphere and (b) the solutions approach the real axis of the complex z-plane.
- 理論物理学刊行会の論文
- 1987-05-25
著者
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Fujisaka Hirokazu
Department Of Applied Analysis And Complex Dynamical Systems Graduate School Of Informatics Kyoto Un
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Inoue Masayoshi
Department Of General Thoracic Surgery (l5) Osaka University Graduate School Of Medicine
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Inoue Masayoshi
Department Of Physics Kagoshima University
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Inoue Masayoshi
Department Of Agriculture Kyoto Prefectural University
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