Dynamic Systems of Shifts in the Space of Piece-Wise Continuous Functions ()

Isaac Kwame Dontwi, William Obeng-Denteh

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

**DOI: **10.4236/apm.2012.26067
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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.

Keywords

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

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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.

Conflicts of Interest

The authors declare no conflicts of interest.

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