R. J. Sacker and G. R. Sell, “Dichotomies for Linear Evolutionary Equations in Banach Spaces,” Journal of Differential Equations, Vol. 113, No. 1, 1994, pp. 17-67. doi:10.1006/jdeq.1994.1113

has been cited by the following article:

• 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.