| Cookie-Cutter集上的Gibbs测度 |
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| 引用本文： | 殷峰丽,王聪. Cookie-Cutter集上的Gibbs测度[J]. 数学年刊A辑(中文版), 2020, 41(2): 213-220 |
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| 作者姓名： | 殷峰丽 王聪 |
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| 作者单位： | 周口师范学院数学与统计学院, 河南,周口~466001.;华中师范大学数学与统计学院, 武汉~430079. |
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| 基金项目： | 国家自然科学基金青年科学基金 (No.,11601175)和周口师范学院高层次人才启动基金(No.,ZKNUC2018007) |
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| 摘 要： | Cookie-Cutter集不仅是动力系统中重要的研究对象,而且是分形中一类重要的集合.而支撑在其上的Gibbs测度对计算分形维数和热力学机制的熵起关键性作用.本文借助于定理2.1构造了支撑在其上的Gibbs测度,并用遍历性证明了该测度的唯一性.
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| 关 键 词： | Cookie-Cutter集 Gibbs测度 Ruelle-Perron-Froebenius定理 遍历测度 |
| 收稿时间： | 2017-07-26 |
| 修稿时间： | 2018-11-07 |
Gibbs Measure of Cookie-Cutter Set |
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| YIN Feng-Li,WANG Cong. Gibbs Measure of Cookie-Cutter Set[J]. Chinese Annals of Mathematics, 2020, 41(2): 213-220 |
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| Authors: | YIN Feng-Li WANG Cong |
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| Affiliation: | School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, Henan, China.; School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China. |
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| Abstract: | The Cookie-Cutter set is not only an important object in the dynamical system,but also a significant set on fractals. Gibbs measure supported by it is the key to the calculation of the fractal dimension and the entropy of thermodynamic formalism. In this paper, the authors construct Gibbs measure by Theorem 2.1, and prove the uniqueness of the measure with ergodicity. |
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| Keywords: | Cookie-Cutter set Gibbs measure Ruelle-Perron-Froebenius theorem Ergodic measure |
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