Combinatorial independence and naive entropy
Dynamical Systems
2021-07-01 v2
Abstract
We study the independence density for finite families of finite tuples of sets for continuous actions of discrete groups on compact metrizable spaces. We use it to show that actions with positive naive entropy are Li-Yorke chaotic and untame. In particular, distal actions have zero naive entropy. This answers a question of Lewis Bowen.
Keywords
Cite
@article{arxiv.1901.02657,
title = {Combinatorial independence and naive entropy},
author = {Hanfeng Li and Zhen Rong},
journal= {arXiv preprint arXiv:1901.02657},
year = {2021}
}
Comments
14 pages. Section 5 is added. To appear in Ergod. Th. Dynam. Sys