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

DOI: 10.4236/apm.2012.26067   PDF   HTML     3,883 Downloads   6,044 Views  

Abstract

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.

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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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