本刊英文版2021年64卷第2期(221-442)摘要

A criterion on a repeller being a null set of any limit measure for stochastic differential equations Lifeng Chen,Zhao Dong&Jifa Jiang 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.