Dynamics with Set-Valued Functions and Coselections

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 T and K and Bellamy's set function Gamma restricted to the hyperspace of singletons.