Open AccessMetric entropy for set-valued maps
Author(s) -
Kendry J. Vivas,
Vı́ctor F. Sirvent
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series 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.