论文标题
随机扩展措施
Random Expansive Measures
论文作者
论文摘要
膨胀性及其概括（测量膨胀，衡量积极的膨胀，连续性膨胀，典型范围）的概念是确定性系统众所周知的，对于研究重要类型的行为，例如混乱的行为，可能是一种有用的特性。这项研究旨在将这些概念扩展到随机上下文中，并证明相对积极熵与随机扩张度量之间的关系，并应用它表明，如果随机动态系统具有正相对拓扑熵，那么$ w $稳定的类别对条件度量的措施为零。我们还证明存在一种概率度量既是不变又膨胀的。此外，我们获得了随机膨胀度量的概念与随机扩张系统之间的关系。
The notion of expansivity and its generalizations (measure expansive, measure positively expansive, continuum-wise expansive, countably-expansive) are well known for deterministic systems and can be a useful property for studying significant type of behavior, such as chaotic one. This study aims to extend these notions into a random context and prove a relationship between relative positive entropy and random expansive measures and apply it to show that if a random dynamical system has positive relative topological entropy then the $w$-stable classes have zero measure for the conditional measures. We also prove that there exists a probability measure that is both invariant and expansive. Moreover, we obtain a relation between the notions of random expansive measures and random countably-expansive systems.
