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

作　　者：Lifeng Chen Zhao Dong Jifa Jiang 

机构地区：[1]Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China [2]RCSDS,Academy of Mathematics and Systems Science,Chinese Academy of Sciences,Beijing 100190,China [3]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Science China Mathematics》2021年第2期221-238,共18页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11771295,11431014,11931004 and 11371252);Key Laboratory of Random Complex Structures and Data Science,Academy of Mathematics and Systems Science,Chinese Academy of Sciences(Grant No.2008DP173182)。

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.

关 键 词：stationary measure limit measure support Lyapunov function repelling limit cycle repelling quasi-periodic orbit 

分 类 号：O211.63[理学—概率论与数理统计]