Naslov
Closed relations with non-zero entropy that generate no periodic points

Autori
Banič, Iztok ; Erceg, Goran ; Kennedy, Judy

Izvornik
Discrete and continuous dynamical systems (1078-0947) 42 (2022), 10; 5137-5166

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Entropy ; topological conjugacy ; periodic points ; finitely generated sets

Sažetak
The paper is motivated by E. Akin's book about dynamical systems and closed relations [1], and by J. Kennedy's and G. Erceg's recent paper about the entropy of closed relations on closed intervals [9]. In present paper, we introduce the entropy of a closed relation G on any compact metric space X and show its basic properties. We also introduce when such a relation G generates a periodic point or finitely generates a Cantor set. Then we show that periodic points, finitely generated Cantor sets, Mahavier products and the entropy of closed relations are preserved by topological conjugations. Among other things, this generalizes the well-known results about the topological conjugacy of continuous mappings. Finally, we prove a theorem, giving sufficient conditions for a closed relation G on [0, 1] to have a non-zero entropy. Then we present various examples of closed relations G on [0, 1] such that (1) the entropy of G is non-zero, (2) no periodic point or exactly one periodic point is generated by G, and (3) no Cantor set is finitely generated by G.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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