English

Measure-theoretic sensitivity via finite partitions

Dynamical Systems 2017-08-22 v2

Abstract

For every positive integer n2n\geq 2, we introduce the concept of measure-theoretic nn-sensitivity for measure-theoretic dynamical systems via finite measurable partitions, and show that an ergodic system is measure-theoretically nn-sensitive but not (n+1)(n+1)-sensitive if and only if its maximal pattern entropy is logn\log n.

Keywords

Cite

@article{arxiv.1606.03649,
  title  = {Measure-theoretic sensitivity via finite partitions},
  author = {Jian Li},
  journal= {arXiv preprint arXiv:1606.03649},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-22T14:23:17.188Z