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We study perturbations of homogeneous linear difference systems over infinite fields with absolute values. The coefficient matrices of the treated systems belong to commutative groups which do not need to be bounded. We present a general limit periodic transformation of an arbitrarily given system such that the obtained system has non-almost periodic solutions. We also formulate corollaries which show how the presented construction of the perturbed system improves and extends known results. [ABSTRACT FROM AUTHOR]

We analyse the solution spaces of limit periodic homogeneous linear difference systems, where the coefficient matrices of the considered systems are taken from a commutative group which does not need to be bounded. In particular, we study such systems whose fundamental matrices are not asymptotically almost periodic or which have solutions vanishing at infinity. We identify a simple condition on the matrix group which guarantees that the studied systems form a dense subset in the space of all considered systems. The obtained results improve previously known theorems about non-almost periodic and non-asymptotically almost periodic solutions. Note that the elements of the coefficient matrices are taken from an infinite field with an absolute value and that the corresponding almost periodic case is treated as well. [ABSTRACT FROM PUBLISHER]

We study limit periodic homogeneous linear difference systems, where the coefficient matrices belong to a bounded group. We find groups of matrices with the property that the systems, which do not possess any non-zero asymptotically almost periodic solution, form a dense subset in the space of all considered systems. Analogously, we analyse almost periodic systems as well. [ABSTRACT FROM AUTHOR]

Almost periodic homogeneous linear difference systems are considered. It is supposed that the coefficient matrices belong to a group. The aim was to find such groups that the systems having no non-trivial almost periodic solution form a dense subset of the set of all considered systems. A closer examination of the used methods reveals that the problem can be treated in such a generality that the entries of coefficient matrices are allowed to belong to any complete metric field. The concepts of transformable and strongly transformable groups of matrices are introduced, and these concepts enable us to derive efficient conditions for determining what matrix groups have the required property. [ABSTRACT FROM PUBLISHER]