Furstenberg families, sensitivity and the space of probability measures

doi:10.1088/1361-6544/aa5495

CSpace

	Furstenberg families, sensitivity and the space of probability measures
	Li, Jie 1,2; Oprocha, Piotr 3,4; Wu, Xinxing 5,6
	2017-03-01
发表期刊	NONLINEARITY
ISSN	0951-7715
卷号	30 期号:3 页码:987-1005
摘要	In this paper we study relations of various types of sensitivity between a t.d.s. (X, T) and t.d.s. (M(X), T-M) induced by (X, T) on the space of probability measures. Among other results, we prove that F -sensitivity of (M(X), TM) implies the same of (X, T) and the converse is also true when F is a filter. We show that (X, T) is multi-sensitive if and only if so is (M(X), TM) and that (X, T) is F -sensitive if and only if (M-n(X), T-M) is F -sensitive (for some/all n is an element of N). We finish the paper providing an example of a minimal syndetically sensitive t.d.s. or a Li-Yorke sensitive t.d.s. such that induced t.d.s. fails to be sensitive.
关键词	Induced space F-sensitivity multi-sensitivity Li-Yorke sensitivity
DOI	10.1088/1361-6544/aa5495
语种	英语
资助项目	NNSF of China[11371339] ; NNSF of China[11571335] ; project 'IT4Innovations excellence in science'[LQ1602] ; National Natural Science Foundation of China[11601449] ; National Natural Science Foundation of China[61601306] ; scientific research starting project of Southwest Petroleum University[2015QHZ029]
WOS研究方向	Mathematics ; Physics
WOS类目	Mathematics, Applied ; Physics, Mathematical
WOS记录号	WOS:000394514800001
出版者	IOP PUBLISHING LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/24784
专题	中国科学院数学与系统科学研究院
通讯作者	Li, Jie
作者单位	1.Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 3.AGH Univ Sci & Technol, Fac Appl Math, Al A Mickiewicza 30, PL-30059 Krakow, Poland 4.Div Univ Ostrava, Inst Res & Applicat Fuzzy Modeling, Natl Supercomp Ctr IT4Innovat, 30 Dubna 22, Ostrava 70103, Czech Republic 5.Southwest Petr Univ, Sch Sci, Chengdu 610500, Sichuan, Peoples R China 6.Southwest Petr Univ, Inst Nonlinear Dynam, Chengdu 610500, Sichuan, Peoples R China
推荐引用方式 GB/T 7714	Li, Jie,Oprocha, Piotr,Wu, Xinxing. Furstenberg families, sensitivity and the space of probability measures[J]. NONLINEARITY,2017,30(3):987-1005.
APA	Li, Jie,Oprocha, Piotr,&Wu, Xinxing.(2017).Furstenberg families, sensitivity and the space of probability measures.NONLINEARITY,30(3),987-1005.
MLA	Li, Jie,et al."Furstenberg families, sensitivity and the space of probability measures".NONLINEARITY 30.3(2017):987-1005.