波恩的一个动态电磁体的公式
Andrzej Biś1, Wojciech Kozłowski1, Agnieszka Marczuk1
1Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Łódź, Poland.
Entropy (Basel, Switzerland)
|November 27, 2024
概括
这项研究扩展了博文的公式,连接了ergodic理论和维度理论,对合规地图的序列. 这项研究证明该公式适用于动态合规电磁体,即一般化动态系统.
科学领域:
- 动态系统 动态系统
- 埃尔戈迪克理论 埃尔戈迪克理论
- 碎形几何学 碎形几何学
背景情况:
- 鲁弗斯·恩 (Rufus Bowen) 在动态系统中建立了一个将 ergodic 理论和维度理论联系起来的公式.
- 原始的恩公式将符合规则的反射器的豪斯多夫维度与单个符合规则的地图的压力函数零相联系.
研究的目的:
- 为了将博文公式扩展到一系列符合规则的地图.
- 在动态电磁体的背景下研究波恩公式的适用性.
主要方法:
- 在一个紧的度量空间上使用连续突起的向后组合的动态电磁体的定义.
- 在轻微假设下开发一个独立的证明,证明Bowen公式的有效性.
主要成果:
- 证明Bowen的公式对于动态合规电磁体是正确的.
- 确定波恩公式对一个在紧空间上的单个合规突移有效的结论.
结论:
- 这些发现概括了动态系统维度理论的一个基本结果.
- 这项研究验证并将恩公式的适用性扩展到更复杂的系统,如合规电磁体.
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