Sufficient conditions for non-zero entropy and finite relations

2022/10/04 by Banic, Iztok, Rogina, Rene Gril, Kennedy, Judy +1
#37B40 #37B45 #37E0 #54C08 #54E45 #54F15 #54F17 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.01880

Abstract

We introduce the notions of returns, dispersions and well-aligned sets for closed relations on compact metric spaces and then we use them to obtain non-trivial sufficient conditions for such a relation to have non-zero entropy. In addition, we give a characterization of finite relations with non-zero entropy in terms of Li-Yorke and DC2-chaos.

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