On the stability in periodic and almost periodic difference systems

In this paper we consider the system of difference equationsxn+1=fn(xn),fn(0)=0,n=0,1,2,…. This system has the trivial (zero) solution xn=0xn=0. Sufficient conditions of its asymptotic stability are obtained in the cases when functions fn(x)fn(x) are periodic and almost periodic in n.