| 殷峰丽,王聪.Cookie-Cutter~集上的~Gibbs~测度[J].数学年刊A辑,2020,41(2):213~220 |
| Cookie-Cutter~集上的~Gibbs~测度 |
| Gibbs Measure of Cookie-Cutter Set |
| Received:July 26, 2017 Revised:November 07, 2018 |
| DOI：10.16205/j.cnki.cama.2020.0015 |
| 中文关键词: Cookie-Cutter集, Gibbs测度, Ruelle-Perron-Froebenius 定理, 遍历测度 |
| 英文关键词:Cookie-Cutter set, Gibbs measure, Ruelle-Perron-Froebenius theorem,Ergodic measure |
| 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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