周期离散动力系统的遍历定理

数学物理学报 ›› 2017, Vol. 37 ›› Issue (3): 534-543.

周期离散动力系统的遍历定理

黄秋灵¹, 史玉明², 张丽娟³

1. 山东财经大学数学与数量经济学院济南 250014;
2. 山东大学数学学院济南 250100;
3. 鲁东大学数学与统计科学学院山东烟台 264025

收稿日期:2015-11-30 修回日期:2016-10-20 出版日期:2017-06-26 发布日期:2017-06-26
通讯作者: 黄秋灵,E-mail:hql_shj@163.com E-mail:hql_shj@163.com
作者简介:史玉明,E-mail:ymshi@sdu.edu.cn;张丽娟,E-mail:zhanglijuan79@163.com
基金资助:
山东省高等学校科技计划项目（J15LI04）、山东省自然科学基金（ZR2011AM002）、国家自然科学基金（61403126）和山东省中青年科学家奖励基金（BS2013SF029）

Ergodic Theorems of Periodic Discrete Dynamical Systems

Huang Qiuling¹, Shi Yuming², Zhang Lijuan³

1. School of Mathematic and Quantitative Economics, Shandong University of Finance and Economics, Jinan 250014;
2 Department of Mathematics, Shandong University, Jinan 250014;
3 School of Mathematics and Statistic Science, Ludong University, Shandong Yantai 264025

Received:2015-11-30 Revised:2016-10-20 Online:2017-06-26 Published:2017-06-26
Supported by:
Supported by the Project of Shandong Province Higher Educational Science and Technology Program (J15LI04), the Natural Science Foundation of Shandong Province (ZR2011AM002), the NSF (61403126) and the Young and Middle-aged Scientists Research Awards Foundation of Shandong Province (BS2013SF029)

摘要/Abstract

摘要： 该文研究周期离散动力系统的遍历定理，把自治离散动力系统的遍历定理推广到周期系统，包括Hilbert空间上的平均遍历定理、von Neumann平均遍历定理和Birkhoff逐点遍历定理.

关键词: 遍历, 遍历定理, 保测变换, 周期离散动力系统

Abstract: This paper focuses on ergodic theorems for periodic discrete systems. The mean ergodic theorem in Hilbert spaces and ergodic theorems for autonomous dynamical systems are generalized to periodic discrete systems, including von Neumann mean ergodic theorem and Birkhoff pointwise ergodic theorem.

Key words: Ergodicity, Ergodic theorem, Measure-preserving transformation, Periodic discrete dynamical system

中图分类号:

黄秋灵, 史玉明, 张丽娟. 周期离散动力系统的遍历定理[J]. 数学物理学报, 2017, 37(3): 534-543.

Huang Qiuling, Shi Yuming, Zhang Lijuan. Ergodic Theorems of Periodic Discrete Dynamical Systems[J]. Acta mathematica scientia,Series A, 2017, 37(3): 534-543.

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