Dynamics with Set-Valued Functions and Coselections

• Camargo, Javier ^[1] ; Macías, Sergio ^[2]
  1. [1] Universidad Industrial de Santander

     Universidad Industrial de Santander

     Colombia

     
  2. [2] Universidad Nacional Autónoma de México

     Universidad Nacional Autónoma de México

     México

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
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• Resumen

  • We study dynamical systems with upper semicontinuous functions and coselections. We define the appropriate versions of dynamic properties on single-valued continuous functions to this setting. We show that some of the definitions given for upper semicontinuous functions resemble the ones for single-valued functions. We consider upper semicontinuous coselections and see their dynamical properties. We use a single-valued function f and compose it with a coselection Θ and define the set-valued function Θf, which we call a Θ-f-coselection. As particular cases of coselections, we use Jones’ set functions T and K and Bellamy’s set function Γ restricted to the hyperspace of singletons.