Author(s)

Isaac Kwame Dontwi, William Obeng-Denteh

Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana.

In this paper we embark on the study of Dynamic Systems of Shifts in the space of piece-wise continuous functions analogue to the known Bebutov system. We give a formal definition of a topological dynamic system in the space of piece-wise continuous functions and show, by way of an example, stability in the sense of Poisson discontinuous function. We prove that a fixed discontinuous function, f, is discontinuous for all its shifts, whereas the trajectory of discontinuous function is not a compact set.

Dynamic System; Shifts; Piecewise Continuous Functions; Compact Sets; Poisson Discontinuous Function

I. Dontwi and W. Obeng-Denteh, "Dynamic Systems of Shifts in the Space of Piece-Wise Continuous Functions," Advances in Pure Mathematics, Vol. 2 No. 6, 2012, pp. 446-449. doi: 10.4236/apm.2012.26067.