Measure-theoretic sensitivity via finite partitions

Abstract

For every positive integer $n\ge 2$, 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 $\log n$.

13 pages. A revision, adding a remark after Proposition 2.5 to explain the proof a litter more

References in corpus (2)

• Mean equicontinuity and mean sensitivity
• Recent development of chaos theory in topological dynamics

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