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arXiv · 1606.03649

Measure-theoretic sensitivity via finite partitions

Jian Li
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Abstract

For every positive integer $n\geq 2$, we introduce the concept of measure-theoretic $n$-sensitivity for measure-theoretic dynamical systems via finite measurable partitions, and show that an ergodic system is measure-theoretically $n$-sensitive but not $(n+1)$-sensitive if and only if its maximal pattern entropy is $\log n$.

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Jian Li. 2017-08-20. Measure-theoretic sensitivity via finite partitions. https://doi.org/10.1088/0951-7715%2F29%2F7%2F2133

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