A criterion on a repeller being a null set of any limit measure for stochastic differential equations

doi:10.1007/s11425-019-1624-8

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	A criterion on a repeller being a null set of any limit measure for stochastic differential equations
	Chen, Lifeng 1,2; Dong, Zhao2,3 ; Jiang, Jifa 1
	2020-02-22
Source Publication	SCIENCE CHINA-MATHEMATICS
ISSN	1674-7283
Pages	18
Abstract	This paper studies limit behaviors of stationary measures for stochastic ordinary differential equations with nondegenerate noise and presents a criterion to guarantee that a repeller with zero Lebesgue measure is a null set of any limit measure. Using this criterion, we first provide a series of nontrivial concrete examples to show that their repelling limit cycles or quasi-periodic orbits are null sets for all limit measures, which deduces that all their limit measures are concentrated on stable equilibria and stable limit cycles or quasi-periodic orbits, and saddles. Interesting open questions on exact supports of limit measures are proposed.
Keyword	stationary measure limit measure support Lyapunov function repelling limit cycle repelling quasi-periodic orbits
DOI	10.1007/s11425-019-1624-8
Indexed By	SCI
Language	英语
Funding Project	National Natural Science Foundation of China[11771295] ; National Natural Science Foundation of China[11431014] ; National Natural Science Foundation of China[11931004] ; National Natural Science Foundation of China[11371252] ; Key Laboratory of Random Complex Structures and Data Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences[2008DP173182]
WOS Research Area	Mathematics
WOS Subject	Mathematics, Applied ; Mathematics
WOS ID	WOS:000516424800001
Publisher	SCIENCE PRESS
Citation statistics
Document Type	期刊论文
Identifier	http://ir.amss.ac.cn/handle/2S8OKBNM/50823
Collection	应用数学研究所
Corresponding Author	Jiang, Jifa
Affiliation	1.Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation GB/T 7714	Chen, Lifeng,Dong, Zhao,Jiang, Jifa. A criterion on a repeller being a null set of any limit measure for stochastic differential equations[J]. SCIENCE CHINA-MATHEMATICS,2020:18.
APA	Chen, Lifeng,Dong, Zhao,&Jiang, Jifa.(2020).A criterion on a repeller being a null set of any limit measure for stochastic differential equations.SCIENCE CHINA-MATHEMATICS,18.
MLA	Chen, Lifeng,et al."A criterion on a repeller being a null set of any limit measure for stochastic differential equations".SCIENCE CHINA-MATHEMATICS (2020):18.

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