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combinatorial independence

Ergodic Theory and Dynamical Systems (1)

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Combinatorial independence and naive entropy
Part of
HANFENG LI, ZHEN RONG
Journal:

Ergodic Theory and Dynamical Systems / Volume 41 / Issue 7 / July 2021

Published online by Cambridge University Press:

15 May 2020, pp. 2136-2147

Print publication:

July 2021
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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.