Combinatorial independence and naive entropy

2019/01/31 by HANFENG LI, Hanfeng Li, Zhen Rong +1 · 6 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topology and Set Theory #Chaotic #Entropy (arrow of time) #Independence (probability theory) #Mathematical Dynamics and Fractals #Metrization theorem #Tuple #math.DS #msc:05D10 #msc:37A35 #msc:37B05 #msc:37B40

paper · pdf · doi:10.1017/etds.2020.39

published in Ergodic Theory and Dynamical Systems 41(7), 2136-2147 (Cambridge University Press) · 14 pages. Section 5 is added. To appear in Ergod. Th. Dynam. Sys

openalex created_date 2019/01/25 · arxiv created 2020/04/16 · openalex publication_date 2020/05/15 · arxiv updated 2021/07/01 · openalex updated_date 2026/08/05

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.

Citations

• Eventual nonsensitivity and tame dynamical systems
• A Characterization of Banach Spaces Containing l 1
• Ergodic properties of discrete dynamical systems and enveloping semigroups
• The dynamical hierarchy for Roelcke precompact Polish groups
• The structure of tame minimal dynamical systems
• Period Three Implies Chaos