Metric entropy for set-valued maps | Zendy

Kendry J. Vivas | Zendy; Vı́ctor F. Sirvent | Zendy

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Metric entropy for set-valued maps

Author(s) -

Kendry J. Vivas,

Vı́ctor F. Sirvent

Publication year - 2022

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2022010

Subject(s) - mathematics , topological entropy , metric space , combinatorics , invariant (physics) , entropy (arrow of time) , discrete mathematics , physics , mathematical physics , quantum mechanics

In this article we define a notion of metric entropy for an invariant measure associated to a set-valued map \begin{document}$ F $\end{document} on a compact metric space \begin{document}$ X $\end{document} . Besides, we describe its main properties and prove the Half Variational Principle , which relates the metric entropy with the notion of topological entropy given in [ 13 ] for this class of maps.

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