| 均匀度理论在分形和混沌研究中的应用 |
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| 引用本文： | 罗传文. 均匀度理论在分形和混沌研究中的应用[J]. 科技导报(北京), 2004, 0(12): 31-35 |
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| 作者姓名： | 罗传文 |
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| 作者单位： | 东北林业大学林学院,博士、教授,哈尔滨,150040 |
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| 摘 要： | 证明了1维和n维欧氏空间中均匀分布的点集的均匀度定理,这是随机性点集空间性质研究的基础,也是混沌点集空间性质研究的基础;将均匀度理论应用于混沌研究中发现,从倍周期分岔到混沌的过程,均匀度（独占线长度）则从确定性收敛变为均方收敛。独战线长度可以用于鉴别混沌的程度,以此方基础定义并计算了混沌强度（chaomerty）。通过混沌强度可以实现对混沌模型和混沌序列的定量评价。混少不了可以解释为：轨道点集均匀化。
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| 关 键 词： | 均匀度定理 混沌 分形 独占球 混沌强度 |
| 文章编号： | 1000-7857(2004)12-0031-05 |
| 修稿时间： | 2004-09-18 |
UNIFORMITY THEORY AND ITS APPLICATION ON FRACTAL AND CHAOS |
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| LUO Chuan-wen. UNIFORMITY THEORY AND ITS APPLICATION ON FRACTAL AND CHAOS[J]. Science & Technology Review, 2004, 0(12): 31-35 |
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| Authors: | LUO Chuan-wen |
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| Abstract: | The uniform index theorems in R1 and Rn were proved , which is the base of spatial property studies on random point set, also that of the spatial property studies on chaos. When uniformity theory was used in the studies on chaos, it was found that the uniform indices of double periodic fork were determinate convergent and that of chaos were convergent in mean square. Monopolized line length can be used to differentiate the intensity of chaos, on which the new word "chaometry" was constructed to show the intensity of chaos. The model and serial on chaos can be quantificationally evaluated by chaometry. Chaos can be interpreted as uniformization of track point set. |
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| Keywords: | uniform index theorem chaos fractal monopolized sphere chaometry |
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