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In this paper, limit periodic and almost periodic homogeneouslinear difference systems are considered. We study the systemsin which the coefficient matrices are taken from a givenbounded group and the elements of the matrices are from aninfinite field with an absolute value. We show a condition onlimit periodic and almost periodic systems which ensures, thatthe considered systems can be transformed into new systemshaving certain properties. The new systems possessnon-asymptotically almost periodic solutions. Thetransformation can be done by arbitrarily small changes.

Asymptotically almost periodic solutions of limit and almost periodic linear difference systems