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 -sequence entropy tuple, the -mean sensitive tuple and the -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}
}