Sufficient conditions for non-zero entropy of closed relations

We introduce the notions of returns and well-aligned sets for closed relations on compact metric spaces and then 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 ter...

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Bibliographic Details
Published in:Ergodic theory and dynamical systems 2024-11, Vol.44 (11), p.3091-3119
Main Authors: BANIČ, IZTOK, GRIL ROGINA, RENE, KENNEDY, JUDY, NALL, VAN
Format: Article
Language:English
Subjects:
Dynamical systems
Entropy
Metric space
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Summary:We introduce the notions of returns and well-aligned sets for closed relations on compact metric spaces and then 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.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2024.11