Measurable n-sensitivity and maximal pattern entropy

Abstract

We introduce the notion of measurable n-sensitivity for measure preserving systems, and study the relation between measurable n-sensitivity and the maximal pattern entropy. We prove that, if (X, B, µ, T) is ergodic, then (X, B, µ, T) is measurable n-sensitive but not measurable (n+1)-sensitive if and only if h_µ^*(T) = log n, where h_µ^* (T) is the maximal pattern entropy of T.

Key words： Measurable n-sensitive; sequence entropy; maximal pattern entropy

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