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

Abstract

In this paper, limit periodic and almost periodic homogeneous linear difference systems are considered. We study the systems in which the coefficient matrices are taken from a given bounded group and the elements of the matrices are from an infinite field with an absolute value. We show a condition on limit periodic and almost periodic systems which ensures, that the considered systems can be transformed into new systems having certain properties. The new systems possess non-asymptotically almost periodic solutions. The transformation can be done by arbitrarily small changes.

Keywords

• limit periodicity
• almost periodicity
• asymptotic almost periodicity
• limit periodic sequences
• almost periodic sequences
• linear difference systems