Abstract
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 \(\Theta \) and define the set-valued function \(\Theta _f\), which we call a \(\Theta \)-f-coselection. As particular cases of coselections, we use Jones’ set functions \({\mathcal {T}}\) and \({\mathcal {K}}\) and Bellamy’s set function \(\Gamma \) restricted to the hyperspace of singletons.
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The authors declare that data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
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The authors thank the referee for the valuable suggestions made that improve the paper.
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Camargo, J., Macías, S. Dynamics with Set-Valued Functions and Coselections. Qual. Theory Dyn. Syst. 21, 25 (2022). https://doi.org/10.1007/s12346-021-00556-9
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DOI: https://doi.org/10.1007/s12346-021-00556-9
Keywords
- Set-valued functions
- Coselections
- Set function \({\mathcal {T}}\)
- Set function \({\mathcal {K}}\)
- Set function \(\Gamma \)
- Transitivity
- Shadowing
- Minimality
- Irreducibility
- Nonwandering points