A new metric for statistical properties of long time behaviors

doi:10.1016/j.jde.2020.02.010

CSpace > 应用数学研究所

	A new metric for statistical properties of long time behaviors
	Zheng, Liqi 1,2; Zheng, Zuohuan1,2,3
	2020-08-05
发表期刊	JOURNAL OF DIFFERENTIAL EQUATIONS
ISSN	0022-0396
卷号	269 期号:4 页码:2741-2773
摘要	Let (X, T) be a topological dynamical system with metric d. We define a new function F(x, y) = by using permutation group S-n. It's shown F(x, y) = exists when x, y. Xare generic points. Applying this function, we prove (X, T) is uniquely ergodic if and only if F(x, y) = 0 for any x, y. X. The characterizations of ergodic measures and physical measures by F(x, y) are given. We introduce the notion of weak mean equicontinuity and prove that (X, T) is weak mean equicontinuous if and only if the time averages are continuous for all f is an element of C(X). (c) 2020 Elsevier Inc. All rights reserved.
关键词	Generic point Unique ergodicity Time average Weak mean equicontinuity
DOI	10.1016/j.jde.2020.02.010
收录类别	SCI
语种	英语
资助项目	NSF of China[11671382] ; CAS Key Project of Frontier Sciences[QYZDJ-SSW-JSC003] ; Key Lab. of Random Complex Structures and Data Sciences CAS ; National Center for Mathematics and Interdisplinary Sciences CAS
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000534488300002
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/51504
专题	应用数学研究所
通讯作者	Zheng, Zuohuan
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Univ Chinese Acad Sci, Beijing 100049, Peoples R China 3.Hainan Normal Univ, Coll Math & Stat, Haikou 571158, Hainan, Peoples R China
推荐引用方式 GB/T 7714	Zheng, Liqi,Zheng, Zuohuan. A new metric for statistical properties of long time behaviors[J]. JOURNAL OF DIFFERENTIAL EQUATIONS,2020,269(4):2741-2773.
APA	Zheng, Liqi,&Zheng, Zuohuan.(2020).A new metric for statistical properties of long time behaviors.JOURNAL OF DIFFERENTIAL EQUATIONS,269(4),2741-2773.
MLA	Zheng, Liqi,et al."A new metric for statistical properties of long time behaviors".JOURNAL OF DIFFERENTIAL EQUATIONS 269.4(2020):2741-2773.