A criterion on a repeller being a null set of any limit measure for stochastic differential equations | |
Chen, Lifeng1,3; Dong, Zhao2,3; Jiang, Jifa1 | |
刊名 | SCIENCE CHINA-MATHEMATICS |
2020-02-22 | |
页码 | 18 |
关键词 | stationary measure limit measure support Lyapunov function repelling limit cycle repelling quasi-periodic orbits |
ISSN号 | 1674-7283 |
DOI | 10.1007/s11425-019-1624-8 |
英文摘要 | 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. |
资助项目 | 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研究方向 | Mathematics |
语种 | 英语 |
出版者 | SCIENCE PRESS |
WOS记录号 | WOS:000516424800001 |
内容类型 | 期刊论文 |
源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/50822] |
专题 | 应用数学研究所 |
通讯作者 | Jiang, Jifa |
作者单位 | 1.Shanghai Normal Univ, Math & Sci Coll, Shanghai 200234, Peoples R China 2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 3.Chinese Acad Sci, Acad Math & Syst Sci, RCSDS, Beijing 100190, Peoples R China |
推荐引用方式 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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