标题： 流动的重缩放扩张测度 显示英文标题

标题： Rescaled expansive measures for flows

摘要： 我们引入了重新缩放扩张测度的概念，以研究流的测度论形式的重新缩放扩张性，特别是在存在奇点的情况下。 通过不同正则性的重参数化，建立了等价定义。 在正熵假设下，我们证明了不变的重新缩放扩张测度的存在性。 在附录中，我们推导了流的Brin-Katok局部熵公式的重新缩放版本，将[7]从无奇点流扩展到可能包含奇点的一般流。 这个框架为理解带有奇点的连续时间动力系统中的熵和扩张性提供了新的工具。 显示英文摘要

摘要： We introduce the notion of rescaled expansive measures to study a measure-theoretic formulation of rescaled expansiveness for flows, particularly in the presence of singularities. Equivalent definitions are established via reparametrizations of different regularities. Under the assumption of positive entropy, we prove the existence of invariant rescaled expansive measures. In the appendix, we derive a rescaled version of the Brin-Katok local entropy formula for flows, extending [7] from nonsingular flows to general flows that may include singularities. This framework provides new tools for understanding entropy and expansiveness in continuous-time dynamical systems with singularities.