TITLE:
Dynamic Systems of Shifts in the Space of Piece-Wise Continuous Functions
AUTHORS:
Isaac Kwame Dontwi, William Obeng-Denteh
KEYWORDS:
Dynamic System; Shifts; Piecewise Continuous Functions; Compact Sets; Poisson Discontinuous Function
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.2 No.6,
November
29,
2012
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.