| Project/Area Number |
61540281
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| Research Category |
Grant-in-Aid for General Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Research Field |
物理学一般
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| Research Institution | Kagoshima University |
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Principal Investigator |
INOUE Masayoshi Faculty of Science, Kagoshima University, 理学部, 教授 (80041234)
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| Co-Investigator(Kenkyū-buntansha) |
YAMADA Tomoji Faculty of Engineering, Kyushu Institute of Technology, 工学部, 教授 (80037928)
FUJISAKA Hirokazu Faculty of Science, Kagoshima University, 理学部, 助教授 (40156849)
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| Project Period (FY) |
1986 – 1987
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| Project Status |
Completed (Fiscal Year 1987)
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| Budget Amount *help |
¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1987: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 1986: ¥500,000 (Direct Cost: ¥500,000)
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| Keywords | Chaos / Fractal / Time Series / Thermodynamics / ストレンジアトラクター / 熱力学 / エントロピー / 乱流 / 自己相似 |
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| Research Abstract |
A study on an analogy in mathematical formalism between a characteritic exponent <lambda>_q 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. Distibution of the solutions of Z[z]=exp[z<lambda>_z]=0 is calculated for several time sequences which are generated by chaotic dynamical systems.
The self-similarity in dynamical and stochastic systems is formulated from a statistical-thermodynamical standpoint. The global structures of the self-similarity are found to be determined by one generating function which plays a role similar to the Helmholtz free energy. The interrelations among fractal measure theories developed for e.g., generalized dimensions of strange sets are clarfied from a unified point of view.
A new statistical-mechanical approach to the temporal in one-dimensional time series generated by a chaotic dynamics is developed. This is done by studying poles of the Fourier transform of the moment M_t[q]=<exp[qtz_t]>,where z_t=[u_1+u_2+...+u_<t-1>]/t is the scale-dependent average. The temporal correlation turn out to be specified with sets of characteristic frequencies. It is shown that the conventional double-time correlation function theory deals only with the limit q->0.
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