一阶格点系统的不变测度与Liouville型方程

数学物理学报 ›› 2020, Vol. 40 ›› Issue (2): 328-339.

一阶格点系统的不变测度与Liouville型方程

李永军¹,桑燕苗²,赵才地^2,*()

¹ 兰州城市学院数学学院兰州 730070
² 温州大学数学系浙江温州 325035

收稿日期:2019-03-07 出版日期:2020-04-26 发布日期:2020-05-21
通讯作者: 赵才地 E-mail:zhaocaidi2013@163.com; zhaocaidi@wzu.edu.cn
基金资助:
国家自然科学基金(11971356);国家自然科学基金(11761044);浙江省自然科学基金(LY17A010011);兰州城市学院重点建设项目(LZCUZDJSXK-201706)

Invariant Measures and Liouville Type Equation for First-Order Lattice System

Yongjun Li¹,Yanmiao Sang²,Caidi Zhao^2,*()

¹ School of Mathematics, Lanzhou City University, Lanzhou 730070
² Department of Mathematics, Wenzhou University, Zhejiang Wenzhou 325035

Received:2019-03-07 Online:2020-04-26 Published:2020-05-21
Contact: Caidi Zhao E-mail:zhaocaidi2013@163.com; zhaocaidi@wzu.edu.cn
Supported by:
the NSFC(11971356);the NSFC(11761044);the NSF of Zhejiang Province(LY17A010011);the Key Constructive Discipline of Lanzhou City University(LZCUZDJSXK-201706)

摘要/Abstract

摘要：

该文讨论一阶格点系统的解在相空间中的概率分布问题.作者先证明该格点系统的解算子生成的过程存在拉回吸引子，然后证明拉回吸引子上存在唯一的Borel不变概率测度，且该不变测度满足Liouville型方程.

关键词: 格点系统, 拉回吸引子, 不变测度, Liouville型方程

Abstract:

This article discusses the probability distribution of solutions in the phase space for the first-order lattice system. The authors first prove the the process generated by the solutions operator of the lattice system possesses a pullback attractor. Then they prove that there is a unique family of invariant probability measures contained in pullback attractor and the measures satisfy a Liouville type equation.

Key words: Lattice system, Pullback attractor, Invariant measure, Liouville type equation

中图分类号:

O175

李永军,桑燕苗,赵才地. 一阶格点系统的不变测度与Liouville型方程[J]. 数学物理学报, 2020, 40(2): 328-339.

Yongjun Li,Yanmiao Sang,Caidi Zhao. Invariant Measures and Liouville Type Equation for First-Order Lattice System[J]. Acta mathematica scientia,Series A, 2020, 40(2): 328-339.

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