| 基于双曲IFSP的概率测度和Dirac测度 |
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| 引用本文： | 江南,马娜娜.基于双曲IFSP的概率测度和Dirac测度[J].吉林大学学报(理学版),2017,55(3):581-586. |
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| 作者姓名： | 江南 马娜娜 |
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| 作者单位： | 1. 西北大学 数学学院, 西安 710127; 2. 西安石油大学 理学院, 西安 710065;3. 西安财经学院 统计学院, 西安 710100 |
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| 摘 要： | 利用Markov算子对测度作用的方法,研究等概率条件下基于双曲迭代函数系的Cantor三分集、Sierpinski直角三角形和Koch曲线等典型分形集中概率测度与Dirac测度的关系,得到了概率相等和概率不等时更一般分形集中概率测度与Dirac测度的关系.
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| 关 键 词： | 概率测度 Dirac测度 吸引子 带概率的双曲迭代函数系(双曲IFSP) |
| 收稿时间： | 2016-05-16 |
Probility Measure and Dirac Measure Based on Hyperbolic IFSP |
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| JIANG Nan,MA Nana.Probility Measure and Dirac Measure Based on Hyperbolic IFSP[J].Journal of Jilin University: Sci Ed,2017,55(3):581-586. |
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| Authors: | JIANG Nan MA Nana |
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| Institution: | 1. School of Mathematics, Northwest University, Xi’an 710127, China;2. School of Science, Xi’an Shiyou University, Xi’an 710065, China;3. School of Statistics, Xi’an University of Finance and Economics, Xi’an 710100, China |
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| Abstract: | Using the method of Markov operator to measure function, we investigated the relationship between probability measure of the typical fractal sets and Dirac measure of Cantor division set, Sierpinski right triangleand Koch curve based on hyperbolic iterated function system under the conditionof equal probability, and obtained the relationship between probability measure and Dirac measure on the more general fractal sets under equal probability and unequal probability, respectively. |
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| Keywords: | hyperbolic iterated function system with probability (hyperbolic IFSP) attractor Dirac measure probability measure |
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