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

作     者：Isaac Kwame Dontwi William Obeng-Denteh 

作者机构：Department of Mathematics Kwame Nkrumah University of Science and Technology Kumasi Ghana 

出 版 物：《Advances in Pure Mathematics》 (理论数学进展（英文）)

年 卷 期：2012年第2卷第6期

页      面：446-449页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Dynamic System Shifts Piecewise Continuous Functions Compact Sets Poisson Discontinuous Function 

摘      要：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.