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I. Assani, “Pointwise Convergence of Ergodic Averages along Cubes,” Journal d’Analyse Mathématique, Vol. 110, No. 1, 2010, pp. 241-269. doi:10.1007/s11854-010-0006-3

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.