加权空间中一阶格点系统的统计解及其 Kolmogorov 熵

数学物理学报 ›› 2023, Vol. 43 ›› Issue (5): 1559-1574.

加权空间中一阶格点系统的统计解及其 Kolmogorov 熵

邹天芳,赵才地^*()

温州大学数理学院浙江温州 325035

收稿日期:2022-10-26 修回日期:2023-04-10 出版日期:2023-10-26 发布日期:2023-08-09
通讯作者: 赵才地 E-mail:zhaocaidi2013@163.com
基金资助:
国家自然科学基金(11971356);浙江省自然科学基金(LY17A010011)

Statistical Solutions and Kolmogorov Entropy for First-Order Lattice Systems in Weighted Spaces

Zou Tianfang,Zhao Caidi^*()

Department of Mathematics, Wenzhou University, Zhejiang Wenzhou 325035

Received:2022-10-26 Revised:2023-04-10 Online:2023-10-26 Published:2023-08-09
Contact: Caidi Zhao E-mail:zhaocaidi2013@163.com
Supported by:
NSF of China(11971356);NSF of Zhejiang Province(LY17A010011)

摘要/Abstract

摘要：

该文研究加权空间中一阶格点系统的统计解及其 Kolmogorov 熵. 文章首先证明一阶格点系统的初值问题在加权空间中具有整体适定性, 且解映射生成一个连续过程并存在一族不变 Borel 概率测度, 接着证明该族不变测度满足 Liouville 定理, 且是该格点系统的统计解, 最后给出了统计解的 Kolmogorov 熵的估计.

关键词: 格点系统, 拉回吸引子, 加权空间, 统计解, Kolmogorov 熵

Abstract:

This article studies the statistical solution and Kolmogorov entropy for first-order lattice systems in weighted spaces. The authors first establish that the initial value problem is global well-posed in weighted spaces and that the continuous process associated to the solution operators possesses a family of invariant Borel probability measures. Then they prove that this family of invariant Borel probability measures meets the Liouville theorem and is a statistical solution of the addressed systems. Finally, they prove the upper bound of the Kolmogorov entropy of the statistical solution.

Key words: Lattice systems, Pullback attractor, Weighted spaces, Statistical solution, Kolmogorov entropy

中图分类号:

O175.8

邹天芳,赵才地. 加权空间中一阶格点系统的统计解及其 Kolmogorov 熵[J]. 数学物理学报, 2023, 43(5): 1559-1574.

Zou Tianfang,Zhao Caidi. Statistical Solutions and Kolmogorov Entropy for First-Order Lattice Systems in Weighted Spaces[J]. Acta mathematica scientia,Series A, 2023, 43(5): 1559-1574.

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