Phase Description Method to Time Averages in dissipative Chaos : Construction of Modified Maps : General and Mathematical Physics
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概要
- 論文の詳細を見る
In order to obtain the description method in terms of the imbedded unstable cycles, we propose a method to construct a modified map whose fixed points correspond to the unstable cycles chosen from all unstable cycles. The modified map enables us to discuss the time averages in 1-D difference systems in a rather unified way. We find that the formula for the time average consists of the two averaging procedures. One is the average over the period of the unstable cycle. The other is the average with the statistical weight including the probability density of the modified map. We also derive the two approximation formulae by assuming that the probability density of the modified map can be represented by the sum of the delta functions, or by the piecewise step-type function. We apply the obtained results to the piecewise linear maps, the logistic map and the Rossler system.
- 理論物理学刊行会の論文
- 1987-05-25
著者
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KOGA Shinji
Diagnostics Research and Development Department, Asahi-Kasei Corporation
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KOGA Shinji
Department of Diagnostics Research & Development, Asahi Chemical Industry Co., Ltd.
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