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Dynamic Systems of Shifts in the Space of Piece-Wise Continuous Functions
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
- 1 Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
- 2 Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Advances in Pure Mathematics·Volume 02 (2012)·Pages 446–449·Published 9 November 2012·DOI10.4236/apm.2012.26067
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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.
KeywordsDynamic SystemShiftsPiecewise Continuous FunctionsCompact SetsPoisson Discontinuous Function
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