遍历理论
数学
随机紧集
吸引子
不变测度
限制设置
概率测度
紧凑空间
独特性
不变(物理)
度量(数据仓库)
动力系统理论
随机动力系统
极限(数学)
离散数学
中心极限定理
基础(拓扑)
随机元素
纯数学
数学分析
随机变量
计算机科学
线性动力系统
物理
统计
量子力学
数据库
线性系统
数学物理
摘要
It is shown that for continuous dynamical systems an analogue of the Poincaré recurrence theorem holds for Ω-limit sets. A similar result is proved for Ω-limit sets of random dynamical systems (RDS) on Polish spaces. This is used to derive that a random set which attracts every (deterministic) compact set has full measure with respect to every invariant probability measure for theRDS. Then we show that a random attractor coincides with the Ω-limit set of a (nonrandom) compact set with probability arbitrarily close to one, and even almost surely in case the base flow is ergodic. This is used to derive uniqueness of attractors, even in case the base flow is not ergodic.
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