English

Sequence entropy tuples and mean sensitive tuples

Dynamical Systems 2023-02-21 v3

Abstract

Using the idea of local entropy theory, we characterize the sequence entropy tuple via mean forms of the sensitive tuple in both topological and measure-theoretical senses. For the measure-theoretical sense, we show that for an ergodic measure-preserving system, the μ\mu-sequence entropy tuple, the μ\mu-mean sensitive tuple and the μ\mu-sensitive in the mean tuple coincide, and give an example to show that the ergodicity condition is necessary. For the topological sense, we show that for a certain class of minimal systems, the mean sensitive tuple is the sequence entropy tuple.

Keywords

Cite

@article{arxiv.2210.16749,
  title  = {Sequence entropy tuples and mean sensitive tuples},
  author = {Jie Li and Chunlin Liu and Siming Tu and Tao Yu},
  journal= {arXiv preprint arXiv:2210.16749},
  year   = {2023}
}
R2 v1 2026-06-28T04:47:04.075Z