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Combinatorial independence and naive entropy

Published online by Cambridge University Press:  15 May 2020

HANFENG LI
Affiliation:
Center of Mathematics, Chongqing University, Chongqing401331, China Department of Mathematics, SUNY at Buffalo, Buffalo, NY14260-2900, USA email [email protected]
ZHEN RONG
Affiliation:
College of Statistics and Mathematics, Inner Mongolia University of Finance and Economics, Hohhot010000, China email [email protected]

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.

Type
Original Article
Copyright
© The Author(s) 2020. Published by Cambridge University Press

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