脉冲分数阶格点系统的不变测度

数学物理学报 ›› 2024, Vol. 44 ›› Issue (6): 1563-1576.

脉冲分数阶格点系统的不变测度

张怡然^*(),黎定仕()

西南交通大学数学学院成都 610031

收稿日期:2024-01-23 修回日期:2024-05-06 出版日期:2024-12-26 发布日期:2024-11-22
通讯作者: ^*张怡然,Email: zhangyiran@my.swjtu.edu.cn
作者简介:黎定仕,Email: lidingshi@swjtu.edu.cn
基金资助:
国家自然科学基金(11971394);国家自然科学基金(12371178);中央引导地方基金(2023ZYD0002)

Invariant Measure of Impulsive Fractional Lattice System

Zhang Yiran^*(),Li Dingshi()

School of Mathematics, Southwest Jiaotong University, Chengdu 610031

Received:2024-01-23 Revised:2024-05-06 Online:2024-12-26 Published:2024-11-22
Supported by:
NSFC(11971394);NSFC(12371178);Fundamental Research Funds for the Central Universities(2023ZYD0002)

摘要/Abstract

摘要：

该文首先证明了分数阶格点系统解的全局适定性, 然后验证了解算子生成的过程是一个连续过程, 并证明该过程具有拉回渐近零性和拉回吸引子, 最后通过广义 Banach 极限构造了该过程的一组 Borel 不变概率测度.

关键词: 不变测度, 脉冲格点系统, 分数阶, 拉回吸引子

Abstract:

This paper first verifies the global validity of the solution of fractional lattice system. Then the paper establishes that the process generated by the solution operator is a continuous process, and it is verified that the process has pull-back asymptotic zero and pull-back attractor, and finally construct a set of Borel invariant probability measures of the process through the generalized Banach limit.

Key words: Invariant measure, Impulsive lattice system, Fractional, Pullback attractor

中图分类号:

O193

张怡然, 黎定仕. 脉冲分数阶格点系统的不变测度[J]. 数学物理学报, 2024, 44(6): 1563-1576.

Zhang Yiran, Li Dingshi. Invariant Measure of Impulsive Fractional Lattice System[J]. Acta mathematica scientia,Series A, 2024, 44(6): 1563-1576.

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