线性斜积半流指数φ-膨胀性的若干刻画

doi:10.3969/j.issn.0253-2778.2020.05.004

中国科学技术大学学报 ›› 2020, Vol. 50 ›› Issue (5): 576-580.DOI: 10.3969/j.issn.0253-2778.2020.05.004

线性斜积半流指数φ-膨胀性的若干刻画

岳田，宋晓秋

1.湖北汽车工业学院理学院,湖北十堰 442002; 2.汽车动力传动与电子控制湖北省重点实验室，湖北十堰 442002；3.中国矿业大学数学学院,江苏徐州 221116

收稿日期:2019-03-04 修回日期:2020-05-27 接受日期:2020-05-27 出版日期:2020-05-31 发布日期:2020-05-27
通讯作者: 岳田
作者简介:岳田(通讯作者),男,1998年生，硕士/讲师.研究方向：微分系统定性理论. E-mail：ytcumt@163.com
基金资助:
国家自然科学基金(11502075)，教育部产学合作协同育人项目(202002137038，202002177010)，汽车动力传动与电子控制湖北省重点实验室开放基金项目( ZDK1202004)资助.

Some characterizations for the exponential φ-expansiveness of linear skew-product semiflows

YUE Tian, SONG Xiaoqiu

1.School of Science, Hubei University of Automotive Technology, Shiyan 442002, China; 2.Hubei Key Laboratory of Automotive Power Train and Electronics Control, Shiyan 442002, China; 3.School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

Received:2019-03-04 Revised:2020-05-27 Accepted:2020-05-27 Online:2020-05-31 Published:2020-05-27

摘要/Abstract

摘要： 研究了Banach空间中线性斜积半流的指数φ-膨胀性. 基于一致指数膨胀性的定义, 引入了Banach空间中线性斜积半流指数φ-膨胀性的概念, 运用数学分析与算子理论得到了指数φ-膨胀性的若干刻画. 所得结果推广和完善了指数稳定性理论中一些已有结果.

关键词: 线性斜积半流, 指数φ-膨胀性, 函数空间

Abstract: The exponential φ-expansiveness of linear skew-product semiflows in Banach space was studied. Based on the definition of uniform exponential expansiveness, a linear skew-product semiflow with exponential φ-expansiveness was presented. Some characterizations for exponential φ-expansiveness were obtained via mathematical analysis and operator theory. The results extend some well-known conclusions in the exponential stability theory.

Key words: linear skew-product semiflows, exponential φ-expansiveness, function spaces

中图分类号:

O175.24

岳田，宋晓秋. 线性斜积半流指数φ-膨胀性的若干刻画[J]. 中国科学技术大学学报, 2020, 50(5): 576-580.

YUE Tian, SONG Xiaoqiu. Some characterizations for the exponential φ-expansiveness of linear skew-product semiflows[J]. Journal of University of Science and Technology of China, 2020, 50(5): 576-580.

线性斜积半流指数φ-膨胀性的若干刻画

Some characterizations for the exponential φ-expansiveness of linear skew-product semiflows

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