A new metric for statistical properties of long time behaviors

doi:10.1016/j.jde.2020.02.010

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	A new metric for statistical properties of long time behaviors
	Zheng, Liqi 1,2; Zheng, Zuohuan 1,2,3
刊名	JOURNAL OF DIFFERENTIAL EQUATIONS
	2020-08-05
卷号	269 期号:4 页码:2741-2773
关键词	Generic point Unique ergodicity Time average Weak mean equicontinuity
ISSN号	0022-0396
DOI	10.1016/j.jde.2020.02.010
英文摘要	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.
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
语种	英语
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
WOS记录号	WOS:000534488300002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/51503]
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.