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arXiv math/06124802006-12-19math.DS

可测量灵敏度

Measurable Sensitivity

Jennifer James, Thomas Koberda, Kathryn Lindsey, Cesar E. Silva, Peter Speh

发表信息：: Proc. Amer. Math. Soc. 136 (2008), no. 10, 3549--3559

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摘要：

我们引入了可测量的灵敏度的概念，灵敏度依赖于初始条件的条件的测量理论版本。它是光混合的结果，意味着变换只有1000个本征值，并且在无限保测度的情况下不存在。与传统的灵敏度依赖概念不同，可测灵敏度可以上升到测度论同构，从而忽略了函数在空集上的行为，消除了对度量选择的依赖。

英文摘要：

We introduce the notion of measurable sensitivity, a measure-theoretic version of the condition of sensitive dependence on initial conditions. It is a consequence of light mixing, implies a transformation has only finitely many eigenvalues, and does not exist in the infinite measure-preserving case. Unlike the traditional notion of sensitive dependence, measurable sensitivity carries up to measure-theoretic isomorphism, thus ignoring the behavior of the function on null sets and eliminating dependence on the choice of metric.

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