Metric entropy for set-valued maps

Kendry J. Vivas; Víctor F. Sirvent

doi:10.3934/dcdsb.2022010

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2022, Volume 27, Issue 11: 6589-6604. Doi: 10.3934/dcdsb.2022010

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Metric entropy for set-valued maps

Kendry J. Vivas^, and
Víctor F. Sirvent

Departamento de Matemáticas, Universidad Católica del Norte, Av. Angamos 0610, Antofagasta, Chile

^*Corresponding author: Kendry J. Vivas
^*Corresponding author: Kendry J. Vivas

Received: September 30, 2021

Revised: November 30, 2021

Early access: January 2022

Published: October 2022

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Abstract

In this article we define a notion of metric entropy for an invariant measure associated to a set-valued map $ F $ on a compact metric space $ X $. 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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Mathematics Subject Classification: Primary: 28D20, 28B20; Secondary: 37B40.

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References

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